(x-8)(x-8)-64

Jasonbradley

2 min read

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Jun 17, 2024

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Factoring and Solving (x-8)(x-8) - 64

This expression represents a quadratic equation that can be factored and solved. Let's break it down:

Simplifying the Expression

1. Expand the square: (x-8)(x-8) is equivalent to (x-8)².
2. Rewrite the expression: Now we have (x-8)² - 64.
3. Recognize the difference of squares: This expression fits the pattern a² - b² where a = (x-8) and b = 8.

Factoring the Difference of Squares

The difference of squares pattern states that a² - b² = (a+b)(a-b). Applying this to our expression:

(x-8)² - 64 = [(x-8) + 8][(x-8) - 8]

Simplifying further:

= (x)(x-16)

Solving the Equation

To solve for x, we set the factored expression equal to zero:

(x)(x-16) = 0

This gives us two possible solutions:

• x = 0
• x = 16

Conclusion

Therefore, the factored form of (x-8)(x-8) - 64 is (x)(x-16), and the solutions to the equation are x = 0 and x = 16.