Jasonbradley
Home

(a-6)2-2 (a-5)(a-7)

2 min read Jun 16, 2024
(a-6)2-2 (a-5)(a-7)

Simplifying the Expression: (a-6)² - 2(a-5)(a-7)

This article will guide you through the process of simplifying the algebraic expression: (a-6)² - 2(a-5)(a-7).

Expanding the Squares and Products

  1. Expand (a-6)²:

    • Remember that (a-6)² is equivalent to (a-6)(a-6).
    • Using the FOIL method (First, Outer, Inner, Last), we get:
    • (a * a) + (a * -6) + (-6 * a) + (-6 * -6) = a² - 12a + 36

  2. Expand 2(a-5)(a-7):

    • First, expand (a-5)(a-7) using FOIL:
    • (a * a) + (a * -7) + (-5 * a) + (-5 * -7) = a² - 12a + 35
    • Then, multiply the result by 2:
    • 2(a² - 12a + 35) = 2a² - 24a + 70

Combining Like Terms

Now we have: a² - 12a + 36 - (2a² - 24a + 70)

  • Distribute the negative sign: a² - 12a + 36 - 2a² + 24a - 70
  • Combine like terms: (a² - 2a²) + (-12a + 24a) + (36 - 70)
  • Simplify: -a² + 12a - 34

Final Simplified Expression

Therefore, the simplified form of the expression (a-6)² - 2(a-5)(a-7) is -a² + 12a - 34.

Related Post

Featured Posts