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(x+5)(x+6)-(x-3)(x+7)

2 min read Jun 16, 2024
(x+5)(x+6)-(x-3)(x+7)

Expanding and Simplifying the Expression (x+5)(x+6)-(x-3)(x+7)

This article will walk through the process of expanding and simplifying the algebraic expression: (x+5)(x+6)-(x-3)(x+7).

Expanding the Expressions

We can simplify this expression by using the distributive property (also known as FOIL method) to expand each of the multiplications:

  • (x+5)(x+6):

    • x * x = x²
    • x * 6 = 6x
    • 5 * x = 5x
    • 5 * 6 = 30
    • (x+5)(x+6) = x² + 6x + 5x + 30

  • (x-3)(x+7):

    • x * x = x²
    • x * 7 = 7x
    • -3 * x = -3x
    • -3 * 7 = -21
    • (x-3)(x+7) = x² + 7x - 3x - 21

Combining the Expanded Expressions

Now we can substitute these expanded expressions back into our original equation:

(x² + 6x + 5x + 30) - (x² + 7x - 3x - 21)

Simplifying the Expression

To simplify, we combine like terms:

  • x² - x² = 0
  • 6x + 5x - 7x + 3x = 7x
  • 30 + 21 = 51

Therefore, the simplified expression is: 7x + 51

Conclusion

By applying the distributive property and combining like terms, we successfully simplified the expression (x+5)(x+6)-(x-3)(x+7) to 7x + 51.

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