Solve The Expression: $ X(x-2) $

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Introduction

Algebraic Expressions are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving a simple algebraic expression: $ x(x-2) $. This expression involves the multiplication of two binomials, and we will use the distributive property to expand and simplify it.

Understanding the Expression

The given expression is $ x(x-2) $. This expression consists of two binomials: $ x $ and $ (x-2) $. To solve this expression, we need to multiply these two binomials using the distributive property.

The Distributive Property

The distributive property is a fundamental concept in algebra that allows us to multiply a single term by two or more terms. It states that for any real numbers $ a $, $ b $, and $ c $, the following equation holds:

a(b+c)=ab+aca(b+c) = ab + ac

Applying the Distributive Property

To solve the expression $ x(x-2) $, we will apply the distributive property by multiplying the first term $ x $ by each term in the second binomial $ (x-2) $.

x(x−2)=x⋅x−x⋅2x(x-2) = x \cdot x - x \cdot 2

Simplifying the Expression

Now that we have applied the distributive property, we can simplify the expression by combining like terms.

x(x−2)=x2−2xx(x-2) = x^2 - 2x

Conclusion

In this article, we have solved the expression $ x(x-2) $ using the distributive property. We have shown that the expression can be simplified to $ x^2 - 2x $. This is a fundamental concept in algebra, and it is essential to understand how to apply the distributive property to solve similar expressions.

Examples and Practice

To reinforce your understanding of the distributive property, try solving the following expressions:

  • $ x(x+3) $
  • $ x(x-5) $
  • $ x(x+2) $

Tips and Tricks

  • When multiplying two binomials, always apply the distributive property by multiplying the first term by each term in the second binomial.
  • When simplifying an expression, always combine like terms.
  • Practice, practice, practice! The more you practice solving expressions, the more comfortable you will become with the distributive property.

Real-World Applications

The distributive property has many real-world applications in fields such as physics, engineering, and economics. For example, in physics, the distributive property is used to calculate the force exerted on an object by multiple forces. In engineering, the distributive property is used to design and optimize systems. In economics, the distributive property is used to calculate the total cost of a product.

History of the Distributive Property

The distributive property has been known since ancient times. The Greek mathematician Euclid (fl. 300 BCE) used the distributive property to prove theorems in his book "Elements". The distributive property was also used by the Indian mathematician Aryabhata (476 CE) to solve algebraic equations.

Conclusion

In conclusion, the distributive property is a fundamental concept in algebra that allows us to multiply a single term by two or more terms. We have shown how to apply the distributive property to solve the expression $ x(x-2) $ and simplify it to $ x^2 - 2x $. This concept has many real-world applications and has been known since ancient times. With practice and patience, you can master the distributive property and become proficient in solving algebraic expressions.

Final Thoughts

The distributive property is a powerful tool that can be used to solve a wide range of algebraic expressions. By mastering the distributive property, you can become proficient in solving equations and inequalities, and you can apply this knowledge to real-world problems. Remember to always practice, practice, practice, and you will become a master of the distributive property in no time.

References

  • Euclid. (fl. 300 BCE). Elements.
  • Aryabhata. (476 CE). Aryabhatiya.
  • Hall, J. D. (2013). Algebra: A Comprehensive Introduction. McGraw-Hill Education.
  • Larson, R. (2015). Algebra and Trigonometry. Cengage Learning.

Further Reading

  • Khan Academy. (n.d.). Distributive Property.
  • Mathway. (n.d.). Distributive Property.
  • Wolfram MathWorld. (n.d.). Distributive Property.

Related Topics

  • Algebraic Expressions
  • Distributive Property
  • Binomials
  • Algebraic Equations
  • Inequalities

Introduction

In our previous article, we solved the expression $ x(x-2) $ using the distributive property. We showed that the expression can be simplified to $ x^2 - 2x $. In this article, we will answer some frequently asked questions about the distributive property and solving algebraic expressions.

Q&A

Q: What is the distributive property?

A: The distributive property is a fundamental concept in algebra that allows us to multiply a single term by two or more terms. It states that for any real numbers $ a $, $ b $, and $ c $, the following equation holds:

a(b+c)=ab+aca(b+c) = ab + ac

Q: How do I apply the distributive property?

A: To apply the distributive property, you need to multiply the first term by each term in the second binomial. For example, to solve the expression $ x(x-2) $, you would multiply the first term $ x $ by each term in the second binomial $ (x-2) $.

Q: What is a binomial?

A: A binomial is an algebraic expression that consists of two terms. For example, $ x-2 $ is a binomial.

Q: How do I simplify an expression?

A: To simplify an expression, you need to combine like terms. Like terms are terms that have the same variable and exponent. For example, in the expression $ x^2 - 2x $, the terms $ x^2 $ and $ -2x $ are like terms.

Q: What is the difference between the distributive property and the commutative property?

A: The distributive property and the commutative property are two different properties in algebra. The distributive property states that for any real numbers $ a $, $ b $, and $ c $, the following equation holds:

a(b+c)=ab+aca(b+c) = ab + ac

The commutative property states that for any real numbers $ a $ and $ b $, the following equation holds:

a+b=b+aa + b = b + a

Q: How do I solve an expression with multiple binomials?

A: To solve an expression with multiple binomials, you need to apply the distributive property multiple times. For example, to solve the expression $ (x+2)(x-3) $, you would first multiply the first term $ x+2 $ by each term in the second binomial $ (x-3) $, and then simplify the resulting expression.

Q: What is the difference between an algebraic expression and an equation?

A: An algebraic expression is a mathematical statement that contains variables and constants. An equation is a mathematical statement that contains an equal sign. For example, $ x^2 - 2x $ is an algebraic expression, while $ x^2 - 2x = 0 $ is an equation.

Q: How do I check my work when solving an expression?

A: To check your work when solving an expression, you need to plug in a value for the variable and see if the expression is true. For example, if you solve the expression $ x^2 - 2x $ and get $ x^2 - 2x = x(x-2) $, you can plug in a value for $ x $, such as $ x = 1 $, and see if the expression is true.

Conclusion

In this article, we have answered some frequently asked questions about the distributive property and solving algebraic expressions. We have shown how to apply the distributive property, simplify expressions, and solve expressions with multiple binomials. We have also discussed the difference between the distributive property and the commutative property, and the difference between an algebraic expression and an equation. With practice and patience, you can master the distributive property and become proficient in solving algebraic expressions.

Final Thoughts

The distributive property is a powerful tool that can be used to solve a wide range of algebraic expressions. By mastering the distributive property, you can become proficient in solving equations and inequalities, and you can apply this knowledge to real-world problems. Remember to always practice, practice, practice, and you will become a master of the distributive property in no time.

References

  • Euclid. (fl. 300 BCE). Elements.
  • Aryabhata. (476 CE). Aryabhatiya.
  • Hall, J. D. (2013). Algebra: A Comprehensive Introduction. McGraw-Hill Education.
  • Larson, R. (2015). Algebra and Trigonometry. Cengage Learning.

Further Reading

  • Khan Academy. (n.d.). Distributive Property.
  • Mathway. (n.d.). Distributive Property.
  • Wolfram MathWorld. (n.d.). Distributive Property.

Related Topics

  • Algebraic Expressions
  • Distributive Property
  • Binomials
  • Algebraic Equations
  • Inequalities