Jasonbradley
Home

(x-2)(x+6)+(x-3)(-4-x)

2 min read Jun 17, 2024
(x-2)(x+6)+(x-3)(-4-x)

Simplifying the Expression: (x-2)(x+6)+(x-3)(-4-x)

This article will guide you through simplifying the algebraic expression (x-2)(x+6)+(x-3)(-4-x).

Expanding the Expression

To begin, we need to expand the expression by using the distributive property (also known as FOIL).

  • For (x-2)(x+6):

    • Multiply the first terms: x * x = x²
    • Multiply the outer terms: x * 6 = 6x
    • Multiply the inner terms: -2 * x = -2x
    • Multiply the last terms: -2 * 6 = -12

  • For (x-3)(-4-x):

    • Multiply the first terms: x * -4 = -4x
    • Multiply the outer terms: x * -x = -x²
    • Multiply the inner terms: -3 * -4 = 12
    • Multiply the last terms: -3 * -x = 3x

Now, our expression looks like this: x² + 6x - 2x - 12 - 4x - x² + 12 + 3x

Combining Like Terms

Next, we combine the like terms:

  • x² terms: x² - x² = 0
  • x terms: 6x - 2x - 4x + 3x = 3x
  • Constant terms: -12 + 12 = 0

The Simplified Expression

After combining like terms, we are left with: 0 + 3x + 0 = 3x

Therefore, the simplified form of the expression (x-2)(x+6)+(x-3)(-4-x) is 3x.

Related Post

Featured Posts