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(3a+4)(2a-3)+(5a-4)(a+2)

2 min read Jun 16, 2024
(3a+4)(2a-3)+(5a-4)(a+2)

Expanding and Simplifying the Expression: (3a+4)(2a-3)+(5a-4)(a+2)

This article aims to guide you through the process of expanding and simplifying the given expression: (3a+4)(2a-3)+(5a-4)(a+2)

Expanding the Expression

The first step involves expanding the two products using the FOIL method (First, Outer, Inner, Last).

  • (3a+4)(2a-3)

    • First: (3a)(2a) = 6a²
    • Outer: (3a)(-3) = -9a
    • Inner: (4)(2a) = 8a
    • Last: (4)(-3) = -12
    • Result: 6a² - 9a + 8a - 12

  • (5a-4)(a+2)

    • First: (5a)(a) = 5a²
    • Outer: (5a)(2) = 10a
    • Inner: (-4)(a) = -4a
    • Last: (-4)(2) = -8
    • Result: 5a² + 10a - 4a - 8

Combining the Expanded Expressions

Now, we combine the two expanded expressions and simplify by grouping like terms:

(6a² - 9a + 8a - 12) + (5a² + 10a - 4a - 8) = 11a² + 5a - 20

Final Simplified Expression

Therefore, the simplified expression for (3a+4)(2a-3)+(5a-4)(a+2) is 11a² + 5a - 20.

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