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(a+3)(a-2)+(a-3)(a+6)

2 min read Jun 16, 2024
(a+3)(a-2)+(a-3)(a+6)

Expanding and Simplifying the Expression: (a+3)(a-2)+(a-3)(a+6)

This article will guide you through the process of expanding and simplifying the given algebraic expression: (a+3)(a-2)+(a-3)(a+6).

Understanding the Problem

We have a sum of two products of binomials. To simplify this expression, we need to:

  1. Expand each product of binomials using the distributive property or FOIL method.
  2. Combine like terms.

Expanding the Binomials

  • (a+3)(a-2)

    Using the FOIL method (First, Outer, Inner, Last):

    • First: a * a = a²
    • Outer: a * -2 = -2a
    • Inner: 3 * a = 3a
    • Last: 3 * -2 = -6

    Combining like terms: a² + a - 6

  • (a-3)(a+6)

    Using the FOIL method:

    • First: a * a = a²
    • Outer: a * 6 = 6a
    • Inner: -3 * a = -3a
    • Last: -3 * 6 = -18

    Combining like terms: a² + 3a - 18

Combining Like Terms

Now we have: (a² + a - 6) + (a² + 3a - 18)

Combining like terms, we get:

2a² + 4a - 24

Final Answer

Therefore, the simplified form of the expression (a+3)(a-2)+(a-3)(a+6) is 2a² + 4a - 24.

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