(2x+10)(x−2)

2 min read Jun 16, 2024

Expanding the Expression (2x+10)(x-2)

This article will guide you through the steps of expanding the expression (2x+10)(x-2).

Understanding the Concept

The expression (2x+10)(x-2) represents the product of two binomials. To expand it, we need to use the distributive property or the FOIL method.

Using the Distributive Property

The distributive property states that a(b + c) = ab + ac. Applying this to our expression:

Distribute (2x+10) over (x-2): (2x+10)(x-2) = 2x(x-2) + 10(x-2)
Distribute again: 2x(x-2) + 10(x-2) = 2x² - 4x + 10x - 20
Combine like terms: 2x² - 4x + 10x - 20 = 2x² + 6x - 20

Using the FOIL Method

FOIL stands for First, Outer, Inner, Last. It's a mnemonic device to help remember the steps involved in multiplying two binomials.

First: Multiply the first terms of each binomial: 2x * x = 2x²
Outer: Multiply the outer terms: 2x * -2 = -4x
Inner: Multiply the inner terms: 10 * x = 10x
Last: Multiply the last terms: 10 * -2 = -20
Combine: 2x² - 4x + 10x - 20 = 2x² + 6x - 20

Conclusion

Both methods lead to the same expanded expression: 2x² + 6x - 20. Expanding algebraic expressions is a fundamental skill in algebra and is essential for solving equations and working with polynomials.