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(x+9)(x-2)+(x+6)(x-3)

2 min read Jun 17, 2024
(x+9)(x-2)+(x+6)(x-3)

Expanding and Simplifying the Expression (x+9)(x-2)+(x+6)(x-3)

This article will guide you through the process of expanding and simplifying the algebraic expression (x+9)(x-2)+(x+6)(x-3).

Expanding the Expression

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

  • (x+9)(x-2):

    • Multiply the first terms: x * x = x²
    • Multiply the outer terms: x * -2 = -2x
    • Multiply the inner terms: 9 * x = 9x
    • Multiply the last terms: 9 * -2 = -18

  • (x+6)(x-3):

    • Multiply the first terms: x * x = x²
    • Multiply the outer terms: x * -3 = -3x
    • Multiply the inner terms: 6 * x = 6x
    • Multiply the last terms: 6 * -3 = -18

Now, the expanded expression looks like this: x² - 2x + 9x - 18 + x² - 3x + 6x - 18

Simplifying the Expression

The next step is to combine like terms:

  • Combine the x² terms: x² + x² = 2x²
  • Combine the x terms: -2x + 9x - 3x + 6x = 10x
  • Combine the constant terms: -18 - 18 = -36

The simplified expression is: 2x² + 10x - 36

Final Result

Therefore, the expanded and simplified form of the expression (x+9)(x-2)+(x+6)(x-3) is 2x² + 10x - 36.

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