# How do you simplify (x-5)(x+3)(x-3)-[4(x^2-4x+1)]^2?

Mar 19, 2018

−16 x^4 +x^3 +201x^2 - 9x + 29

#### Explanation:

Simplify
(x−5)(x+3)(x−3)−[4(x^2−4x+1)]^2

I don't know if you'd call it "simplifying," but you can clear those parentheses.

1) Multiply $\left(x + 3\right) \left(x - 3\right)$ by recognizing the binomials as the factors of a Difference of Two Squares
After you have multiplied the binomials by memorization, you get this:
(x−5)(x^2 - 9)−[4(x^2−4x+1)]^2

2) Clear the parentheses inside the brackets by distributing the $4$
(x−5)(x^2 - 9)−[4x^2−16x+4]^2

3) Clear the brackets by raising all the powers inside by the power of $2$ outside.
To raise a power to a power, multiply the exponents.
(x−5)(x^2 - 9)−[4^2 x^4−16^2 x^2+4^2]

4) Evaluate the constants
(x−5)(x^2 - 9)−[16  x^4−196 x^2+16]

5) Clear the brackets by distributing the minus sign
(x−5)(x^2 - 9)−16 x^4+196 x^2-16

6) Clear the parentheses by multiplying the binomials
x^3 +5x^2 - 9x + 45−16 x^4+196 x^2-16

7) Group like terms
−16 x^4 +x^3    (+5x^2 +196 x^2)   - 9x     (+ 45-16)

8) Combine like terms
−16 x^4 +x^3 +201x^2 - 9x + 29 $\leftarrow$ answer