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(x+4)(x+7)+(x+8)(x+5)

2 min read Jun 16, 2024
(x+4)(x+7)+(x+8)(x+5)

Expanding and Simplifying the Expression (x+4)(x+7)+(x+8)(x+5)

This article will guide you through the process of expanding and simplifying the expression (x+4)(x+7)+(x+8)(x+5).

Step 1: Expanding the Products

We begin by expanding each of the products using the FOIL method (First, Outer, Inner, Last):

  • (x+4)(x+7)

    • First: x * x = x²
    • Outer: x * 7 = 7x
    • Inner: 4 * x = 4x
    • Last: 4 * 7 = 28
    • Combined: x² + 7x + 4x + 28 = x² + 11x + 28

  • (x+8)(x+5)

    • First: x * x = x²
    • Outer: x * 5 = 5x
    • Inner: 8 * x = 8x
    • Last: 8 * 5 = 40
    • Combined: x² + 5x + 8x + 40 = x² + 13x + 40

Step 2: Combining Like Terms

Now that we've expanded both products, we can combine the like terms:

  • x² + 11x + 28 + x² + 13x + 40
  • (x² + x²) + (11x + 13x) + (28 + 40)

Step 3: Simplifying the Expression

Finally, we simplify the expression by combining the coefficients:

  • 2x² + 24x + 68

Conclusion

Therefore, the simplified form of the expression (x+4)(x+7)+(x+8)(x+5) is 2x² + 24x + 68.

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