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(x-7)^2+(x+5)(x-5)

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

Simplifying the Expression (x-7)^2 + (x+5)(x-5)

This article will guide you through the process of simplifying the expression (x-7)^2 + (x+5)(x-5).

Understanding the Expression

The expression consists of two terms:

  • (x-7)^2: This is a squared binomial, which means we need to multiply the binomial by itself.
  • (x+5)(x-5): This is a product of two binomials in the form (a+b)(a-b), which is a special product known as the "difference of squares".

Simplifying the Expression

Let's simplify each term individually:

  1. (x-7)^2:

    • Expand the square: (x-7)(x-7)
    • Apply the FOIL method (First, Outer, Inner, Last) to multiply the binomials:
      • x * x = x²
      • x * -7 = -7x
      • -7 * x = -7x
      • -7 * -7 = 49
    • Combine like terms: x² - 7x - 7x + 49 = x² - 14x + 49

  2. (x+5)(x-5):

    • This is a difference of squares pattern, which simplifies to: a² - b²
    • In this case, a = x and b = 5.
    • Therefore, (x+5)(x-5) = x² - 5² = x² - 25

Combining the Simplified Terms

Now we have simplified both terms:

  • (x-7)² = x² - 14x + 49
  • (x+5)(x-5) = x² - 25

Combining these simplified terms, we get: (x-7)² + (x+5)(x-5) = (x² - 14x + 49) + (x² - 25)

Finally, we combine like terms: x² - 14x + 49 + x² - 25 = 2x² - 14x + 24

Conclusion

Therefore, the simplified form of the expression (x-7)² + (x+5)(x-5) is 2x² - 14x + 24.

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