Evaluate The Expression: 9 2 − 4 2 9^2 - 4^2 9 2 − 4 2

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Introduction

In mathematics, the expression $9^2 - 4^2$ is a simple algebraic expression that can be evaluated using the difference of squares formula. The difference of squares formula is a fundamental concept in algebra that allows us to simplify expressions of the form $a^2 - b^2$. In this article, we will evaluate the expression $9^2 - 4^2$ using the difference of squares formula and explore its applications in mathematics.

The Difference of Squares Formula

The difference of squares formula is a mathematical formula that states:

$a^2 - b^2 = (a + b)(a - b)$

This formula can be used to simplify expressions of the form $a^2 - b^2$ by factoring them into the product of two binomials. The difference of squares formula is a powerful tool in algebra that can be used to solve equations and simplify expressions.

Evaluating the Expression $9^2 - 4^2$

To evaluate the expression $9^2 - 4^2$, we can use the difference of squares formula. We can rewrite the expression as:

$9^2 - 4^2 = (9 + 4)(9 - 4)$

Using the difference of squares formula, we can simplify the expression as:

$9^2 - 4^2 = (13)(5)$

Evaluating the product, we get:

$9^2 - 4^2 = 65$

Therefore, the value of the expression $9^2 - 4^2$ is 65.

Applications of the Difference of Squares Formula

The difference of squares formula has many applications in mathematics. It can be used to solve equations, simplify expressions, and factor polynomials. The formula is also used in algebraic geometry to study the properties of curves and surfaces.

Example 1: Solving an Equation

Consider the equation:

$x^2 - 16 = 0$

We can use the difference of squares formula to solve this equation. We can rewrite the equation as:

$x^2 - 16 = (x + 4)(x - 4)$

Setting each factor equal to zero, we get:

$x + 4 = 0$ or $x - 4 = 0$

Solving for x, we get:

$x = -4$ or $x = 4$

Therefore, the solutions to the equation are x = -4 and x = 4.

Example 2: Simplifying an Expression

Consider the expression:

$25^2 - 9^2$

We can use the difference of squares formula to simplify this expression. We can rewrite the expression as:

$25^2 - 9^2 = (25 + 9)(25 - 9)$

Using the difference of squares formula, we can simplify the expression as:

$25^2 - 9^2 = (34)(16)$

Evaluating the product, we get:

$25^2 - 9^2 = 544$

Therefore, the value of the expression $25^2 - 9^2$ is 544.

Conclusion

In this article, we evaluated the expression $9^2 - 4^2$ using the difference of squares formula. We also explored the applications of the formula in mathematics, including solving equations and simplifying expressions. The difference of squares formula is a powerful tool in algebra that can be used to solve equations and simplify expressions.

Final Thoughts

The difference of squares formula is a fundamental concept in algebra that can be used to simplify expressions of the form $a^2 - b^2$. It is a powerful tool that can be used to solve equations and simplify expressions. In this article, we evaluated the expression $9^2 - 4^2$ using the difference of squares formula and explored its applications in mathematics.

References

• [1] "Algebra" by Michael Artin
• [2] "Calculus" by Michael Spivak
• [3] "Linear Algebra" by Jim Hefferon

Keywords

• Difference of squares formula
• Algebra
• Mathematics
• Equations
• Expressions
• Factorization
• Simplification

Related Topics

• [1] "Solving Equations"
• [2] "Simplifying Expressions"
• [3] "Factorization"
• [4] "Algebraic Geometry"
• [5] "Calculus"

Further Reading

• [1] "Algebra" by Michael Artin
• [2] "Calculus" by Michael Spivak
• [3] "Linear Algebra" by Jim Hefferon
• [4] "Mathematics for Computer Science" by Eric Lehman
• [5] "Discrete Mathematics" by Kenneth Rosen
  

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Introduction

In our previous article, we evaluated the expression $9^2 - 4^2$ using the difference of squares formula. In this article, we will answer some frequently asked questions about evaluating the expression $9^2 - 4^2$.

Q1: What is the difference of squares formula?

A1: The difference of squares formula is a mathematical formula that states:

$a^2 - b^2 = (a + b)(a - b)$

This formula can be used to simplify expressions of the form $a^2 - b^2$ by factoring them into the product of two binomials.

Q2: How do I apply the difference of squares formula to evaluate the expression $9^2 - 4^2$?

A2: To apply the difference of squares formula, you can rewrite the expression as:

$9^2 - 4^2 = (9 + 4)(9 - 4)$

Using the difference of squares formula, you can simplify the expression as:

$9^2 - 4^2 = (13)(5)$

Evaluating the product, you get:

$9^2 - 4^2 = 65$

Q3: What are some common mistakes to avoid when applying the difference of squares formula?

A3: Some common mistakes to avoid when applying the difference of squares formula include:

• Not recognizing that the expression is in the form $a^2 - b^2$
• Not rewriting the expression in the correct form
• Not simplifying the expression correctly
• Not evaluating the product correctly

Q4: Can the difference of squares formula be used to solve equations?

A4: Yes, the difference of squares formula can be used to solve equations. For example, consider the equation:

$x^2 - 16 = 0$

We can use the difference of squares formula to solve this equation. We can rewrite the equation as:

$x^2 - 16 = (x + 4)(x - 4)$

Setting each factor equal to zero, we get:

$x + 4 = 0$ or $x - 4 = 0$

Solving for x, we get:

$x = -4$ or $x = 4$

Q5: Can the difference of squares formula be used to simplify expressions?

A5: Yes, the difference of squares formula can be used to simplify expressions. For example, consider the expression:

$25^2 - 9^2$

We can use the difference of squares formula to simplify this expression. We can rewrite the expression as:

$25^2 - 9^2 = (25 + 9)(25 - 9)$

Using the difference of squares formula, we can simplify the expression as:

$25^2 - 9^2 = (34)(16)$

Evaluating the product, we get:

$25^2 - 9^2 = 544$

Q6: What are some real-world applications of the difference of squares formula?

A6: Some real-world applications of the difference of squares formula include:

• Solving equations in physics and engineering
• Simplifying expressions in computer science and programming
• Factoring polynomials in algebra and geometry
• Solving problems in finance and economics

Q7: Can the difference of squares formula be used to solve quadratic equations?

A7: Yes, the difference of squares formula can be used to solve quadratic equations. For example, consider the quadratic equation:

$x^2 - 6x + 8 = 0$

We can use the difference of squares formula to solve this equation. We can rewrite the equation as:

$x^2 - 6x + 8 = (x - 4)(x - 2)$

Setting each factor equal to zero, we get:

$x - 4 = 0$ or $x - 2 = 0$

Solving for x, we get:

$x = 4$ or $x = 2$

Q8: Can the difference of squares formula be used to simplify complex expressions?

A8: Yes, the difference of squares formula can be used to simplify complex expressions. For example, consider the expression:

$(x + 3)^2 - (x - 2)^2$

We can use the difference of squares formula to simplify this expression. We can rewrite the expression as:

$(x + 3)^2 - (x - 2)^2 = ((x + 3) + (x - 2))((x + 3) - (x - 2))$

Using the difference of squares formula, we can simplify the expression as:

$(x + 3)^2 - (x - 2)^2 = (2x + 1)(4)$

Evaluating the product, we get:

$(x + 3)^2 - (x - 2)^2 = 8x + 4$

Conclusion

In this article, we answered some frequently asked questions about evaluating the expression $9^2 - 4^2$ using the difference of squares formula. We hope that this article has been helpful in clarifying any doubts you may have had about the difference of squares formula.

Final Thoughts

The difference of squares formula is a powerful tool in algebra that can be used to simplify expressions of the form $a^2 - b^2$. It is a fundamental concept in algebra that can be used to solve equations and simplify expressions. In this article, we answered some frequently asked questions about evaluating the expression $9^2 - 4^2$ using the difference of squares formula.

References

• [1] "Algebra" by Michael Artin
• [2] "Calculus" by Michael Spivak
• [3] "Linear Algebra" by Jim Hefferon

Keywords

• Difference of squares formula
• Algebra
• Mathematics
• Equations
• Expressions
• Factorization
• Simplification

Related Topics

• [1] "Solving Equations"
• [2] "Simplifying Expressions"
• [3] "Factorization"
• [4] "Algebraic Geometry"
• [5] "Calculus"

Further Reading

• [1] "Algebra" by Michael Artin
• [2] "Calculus" by Michael Spivak
• [3] "Linear Algebra" by Jim Hefferon
• [4] "Mathematics for Computer Science" by Eric Lehman
• [5] "Discrete Mathematics" by Kenneth Rosen