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(x+7)(x-5)+(x+1)(x+4)

2 min read Jun 17, 2024
(x+7)(x-5)+(x+1)(x+4)

Expanding and Simplifying the Expression: (x+7)(x-5) + (x+1)(x+4)

This article will walk through the steps of expanding and simplifying the algebraic expression: (x+7)(x-5) + (x+1)(x+4).

Expanding the Products

We can expand the expression by using the FOIL method (First, Outer, Inner, Last) for each pair of parentheses.

  • (x+7)(x-5):

    • First: x * x = x²
    • Outer: x * -5 = -5x
    • Inner: 7 * x = 7x
    • Last: 7 * -5 = -35

  • (x+1)(x+4):

    • First: x * x = x²
    • Outer: x * 4 = 4x
    • Inner: 1 * x = x
    • Last: 1 * 4 = 4

Combining the results, we get: x² - 5x + 7x - 35 + x² + 4x + x + 4

Simplifying the Expression

Now we combine like terms to simplify the expression:

  • x² + x² = 2x²
  • -5x + 7x + 4x + x = 7x
  • -35 + 4 = -31

Therefore, the simplified expression is: 2x² + 7x - 31

Final Answer

The expanded and simplified form of the expression (x+7)(x-5) + (x+1)(x+4) is 2x² + 7x - 31.

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