(x-2)(-5x^(2)+x)=(x)(-5x^(2))+(x)(x)+(-2)(-5x^(2))+(-2)(x)

Jasonbradley

2 min read

·

Jun 17, 2024

58

Share

Expanding Algebraic Expressions: A Step-by-Step Guide

The equation (x-2)(-5x^(2)+x)=(x)(-5x^(2))+(x)(x)+(-2)(-5x^(2))+(-2)(x) demonstrates the process of expanding an algebraic expression. This process is crucial for simplifying equations and solving for unknown variables. Let's break down this equation step by step to understand the underlying principles.

The Distributive Property

The key to expanding this expression lies in the distributive property. This property states that multiplying a sum by a number is the same as multiplying each term of the sum by that number. In our example, we have two sums:

• (x - 2)
• (-5x^(2) + x)

To expand the expression, we multiply each term of the first sum by each term of the second sum:

Step 1: Multiply x from the first sum by each term of the second sum:

• (x)(-5x^(2)) = -5x^(3)
• (x)(x) = x^(2)

Step 2: Multiply -2 from the first sum by each term of the second sum:

• (-2)(-5x^(2)) = 10x^(2)
• (-2)(x) = -2x

Step 3: Combine all the resulting terms:

-5x^(3) + x^(2) + 10x^(2) - 2x

Simplifying the Expression

The final step involves combining like terms:

-5x^(3) + 11x^(2) - 2x

This simplified expression is the expanded form of the original equation.

Conclusion

Expanding algebraic expressions using the distributive property is a fundamental skill in algebra. By breaking down the process into manageable steps, you can confidently manipulate and simplify complex expressions.