Simplify The Expression: { (5x - 2)^2$}$

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Introduction

In mathematics, simplifying algebraic expressions is a crucial skill that helps in solving equations and inequalities. One of the most common methods of simplifying expressions is by using the formula for expanding a squared binomial. In this article, we will focus on simplifying the expression {(5x - 2)^2$}$ using the formula for expanding a squared binomial.

Understanding the Formula for Expanding a Squared Binomial

The formula for expanding a squared binomial is given by:

(a+b)2=a2+2ab+b2{(a + b)^2 = a^2 + 2ab + b^2}

This formula can be used to expand any squared binomial, where 'a' and 'b' are the two terms being squared.

Applying the Formula to the Given Expression

To simplify the expression {(5x - 2)^2$}$, we can use the formula for expanding a squared binomial. Here, 'a' is ${5x\$} and 'b' is −2${-2\$}.

Step 1: Square the First Term

The first step in expanding the squared binomial is to square the first term, which is ${5x\$}. This can be done by squaring the coefficient and the variable separately.

(5x)2=25x2{(5x)^2 = 25x^2}

Step 2: Multiply the First Term by the Second Term

The next step is to multiply the first term by the second term. This can be done by multiplying the coefficient of the first term by the second term, and then multiplying the variable of the first term by the second term.

5x×−2=−10x{5x \times -2 = -10x}

Step 3: Square the Second Term

The final step is to square the second term, which is −2${-2\$}. This can be done by squaring the coefficient and the variable separately.

(−2)2=4{(-2)^2 = 4}

Step 4: Combine the Terms

Now that we have squared the first term, multiplied the first term by the second term, and squared the second term, we can combine the terms to simplify the expression.

(5x−2)2=25x2+2×5x×−2+4{(5x - 2)^2 = 25x^2 + 2 \times 5x \times -2 + 4}

Step 5: Simplify the Expression

The final step is to simplify the expression by combining like terms.

(5x−2)2=25x2−20x+4{(5x - 2)^2 = 25x^2 - 20x + 4}

Conclusion

In this article, we have simplified the expression {(5x - 2)^2$}$ using the formula for expanding a squared binomial. We have broken down the process into five steps, and have shown how to square the first term, multiply the first term by the second term, square the second term, combine the terms, and simplify the expression. By following these steps, we can simplify any squared binomial expression.

Frequently Asked Questions

  • What is the formula for expanding a squared binomial?

The formula for expanding a squared binomial is given by:

(a+b)2=a2+2ab+b2{(a + b)^2 = a^2 + 2ab + b^2}

  • How do I simplify a squared binomial expression?

To simplify a squared binomial expression, you can use the formula for expanding a squared binomial. This involves squaring the first term, multiplying the first term by the second term, squaring the second term, combining the terms, and simplifying the expression.

  • What is the simplified form of the expression {(5x - 2)^2$}$?

The simplified form of the expression {(5x - 2)^2$}$ is ${25x^2 - 20x + 4\$}.

Final Thoughts

Simplifying algebraic expressions is a crucial skill that helps in solving equations and inequalities. By using the formula for expanding a squared binomial, we can simplify any squared binomial expression. In this article, we have shown how to simplify the expression {(5x - 2)^2$}$ using the formula for expanding a squared binomial. We hope that this article has provided you with a clear understanding of how to simplify squared binomial expressions.

Additional Resources

  • Algebraic Expressions

Algebraic expressions are mathematical expressions that contain variables and constants. They can be simplified using various methods, including the formula for expanding a squared binomial.

  • Simplifying Algebraic Expressions

Simplifying algebraic expressions is a crucial skill that helps in solving equations and inequalities. It involves using various methods, including the formula for expanding a squared binomial.

  • Mathematics

Mathematics is a branch of science that deals with numbers, quantities, and shapes. It involves various branches, including algebra, geometry, and calculus.

References

  • Algebra

Algebra is a branch of mathematics that deals with variables and constants. It involves solving equations and inequalities, and simplifying algebraic expressions.

  • Geometry

Geometry is a branch of mathematics that deals with shapes and sizes. It involves calculating perimeter, area, and volume of various shapes.

  • Calculus

Calculus is a branch of mathematics that deals with rates of change and accumulation. It involves calculating derivatives and integrals.

Glossary

  • Algebraic Expression

An algebraic expression is a mathematical expression that contains variables and constants.

  • Simplified Expression

A simplified expression is an algebraic expression that has been simplified using various methods, including the formula for expanding a squared binomial.

  • Squared Binomial

A squared binomial is an algebraic expression that contains two terms being squared.

  • Coefficient

A coefficient is a number that is multiplied by a variable in an algebraic expression.

  • Variable

A variable is a letter or symbol that represents a value in an algebraic expression.

  • Constant

A constant is a number that does not change in an algebraic expression.

Related Articles

  • Simplifying Algebraic Expressions

Simplifying algebraic expressions is a crucial skill that helps in solving equations and inequalities. It involves using various methods, including the formula for expanding a squared binomial.

  • Algebraic Identities

Algebraic identities are mathematical expressions that are true for all values of the variables. They can be used to simplify algebraic expressions.

  • Mathematical Operations

Mathematical operations are the basic operations that are used in mathematics, including addition, subtraction, multiplication, and division.

Tags

  • Algebraic Expressions
  • Simplifying Algebraic Expressions
  • Squared Binomial
  • Coefficient
  • Variable
  • Constant
  • Mathematics
  • Algebra
  • Geometry
  • Calculus

Introduction

In our previous article, we simplified the expression {(5x - 2)^2$}$ using the formula for expanding a squared binomial. In this article, we will answer some frequently asked questions related to simplifying algebraic expressions.

Q&A

Q1: What is the formula for expanding a squared binomial?

A1: The formula for expanding a squared binomial is given by:

(a+b)2=a2+2ab+b2{(a + b)^2 = a^2 + 2ab + b^2}

Q2: How do I simplify a squared binomial expression?

A2: To simplify a squared binomial expression, you can use the formula for expanding a squared binomial. This involves squaring the first term, multiplying the first term by the second term, squaring the second term, combining the terms, and simplifying the expression.

Q3: What is the simplified form of the expression {(5x - 2)^2$}$?

A3: The simplified form of the expression {(5x - 2)^2$}$ is ${25x^2 - 20x + 4\$}.

Q4: Can I use the formula for expanding a squared binomial to simplify any algebraic expression?

A4: No, the formula for expanding a squared binomial can only be used to simplify squared binomial expressions. However, you can use other methods to simplify other types of algebraic expressions.

Q5: What is the difference between a squared binomial and a squared trinomial?

A5: A squared binomial is an algebraic expression that contains two terms being squared, while a squared trinomial is an algebraic expression that contains three terms being squared.

Q6: How do I simplify a squared trinomial expression?

A6: To simplify a squared trinomial expression, you can use the formula for expanding a squared trinomial, which is given by:

(a+b+c)2=a2+2ab+2ac+b2+2bc+c2{(a + b + c)^2 = a^2 + 2ab + 2ac + b^2 + 2bc + c^2}

Q7: Can I use the formula for expanding a squared binomial to simplify a squared trinomial expression?

A7: No, the formula for expanding a squared binomial cannot be used to simplify a squared trinomial expression. You need to use the formula for expanding a squared trinomial to simplify a squared trinomial expression.

Q8: What is the difference between a coefficient and a variable?

A8: A coefficient is a number that is multiplied by a variable in an algebraic expression, while a variable is a letter or symbol that represents a value in an algebraic expression.

Q9: How do I simplify an algebraic expression that contains variables and constants?

A9: To simplify an algebraic expression that contains variables and constants, you can use various methods, including combining like terms, factoring, and using the formula for expanding a squared binomial.

Q10: Can I use the formula for expanding a squared binomial to simplify an algebraic expression that contains variables and constants?

A10: Yes, you can use the formula for expanding a squared binomial to simplify an algebraic expression that contains variables and constants, but only if the expression is a squared binomial.

Conclusion

In this article, we have answered some frequently asked questions related to simplifying algebraic expressions. We hope that this article has provided you with a clear understanding of how to simplify squared binomial expressions and other types of algebraic expressions.

Frequently Asked Questions

  • What is the formula for expanding a squared binomial?

The formula for expanding a squared binomial is given by:

(a+b)2=a2+2ab+b2{(a + b)^2 = a^2 + 2ab + b^2}

  • How do I simplify a squared binomial expression?

To simplify a squared binomial expression, you can use the formula for expanding a squared binomial. This involves squaring the first term, multiplying the first term by the second term, squaring the second term, combining the terms, and simplifying the expression.

  • What is the simplified form of the expression {(5x - 2)^2$}$?

The simplified form of the expression {(5x - 2)^2$}$ is ${25x^2 - 20x + 4\$}.

Final Thoughts

Simplifying algebraic expressions is a crucial skill that helps in solving equations and inequalities. By using the formula for expanding a squared binomial, we can simplify any squared binomial expression. In this article, we have answered some frequently asked questions related to simplifying algebraic expressions.

Additional Resources

  • Algebraic Expressions

Algebraic expressions are mathematical expressions that contain variables and constants. They can be simplified using various methods, including the formula for expanding a squared binomial.

  • Simplifying Algebraic Expressions

Simplifying algebraic expressions is a crucial skill that helps in solving equations and inequalities. It involves using various methods, including the formula for expanding a squared binomial.

  • Mathematics

Mathematics is a branch of science that deals with numbers, quantities, and shapes. It involves various branches, including algebra, geometry, and calculus.

References

  • Algebra

Algebra is a branch of mathematics that deals with variables and constants. It involves solving equations and inequalities, and simplifying algebraic expressions.

  • Geometry

Geometry is a branch of mathematics that deals with shapes and sizes. It involves calculating perimeter, area, and volume of various shapes.

  • Calculus

Calculus is a branch of mathematics that deals with rates of change and accumulation. It involves calculating derivatives and integrals.

Glossary

  • Algebraic Expression

An algebraic expression is a mathematical expression that contains variables and constants.

  • Simplified Expression

A simplified expression is an algebraic expression that has been simplified using various methods, including the formula for expanding a squared binomial.

  • Squared Binomial

A squared binomial is an algebraic expression that contains two terms being squared.

  • Coefficient

A coefficient is a number that is multiplied by a variable in an algebraic expression.

  • Variable

A variable is a letter or symbol that represents a value in an algebraic expression.

  • Constant

A constant is a number that does not change in an algebraic expression.

Related Articles

  • Simplifying Algebraic Expressions

Simplifying algebraic expressions is a crucial skill that helps in solving equations and inequalities. It involves using various methods, including the formula for expanding a squared binomial.

  • Algebraic Identities

Algebraic identities are mathematical expressions that are true for all values of the variables. They can be used to simplify algebraic expressions.

  • Mathematical Operations

Mathematical operations are the basic operations that are used in mathematics, including addition, subtraction, multiplication, and division.

Tags

  • Algebraic Expressions
  • Simplifying Algebraic Expressions
  • Squared Binomial
  • Coefficient
  • Variable
  • Constant
  • Mathematics
  • Algebra
  • Geometry
  • Calculus