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andrey2020 [161]
3 years ago
7

Given the expression: 5x10 − 80x2 Part A: Rewrite the expression by factoring out the greatest common factor. Part B: Factor the

entire expression completely. Show the steps of your work.
Mathematics
1 answer:
Darina [25.2K]3 years ago
3 0

Answer:

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

Step-by-step explanation:

5x^10 − 80x^2

The greatest common factor is 5x^2

5x^2 ( x^8 - 16)

Rewriting the parentheses

5x^2 ( x^4 ^2 - 4^2)

We notice the difference of squares (a^2 -b^2) = (a-b)(a+b)

5x^2 ( x^4 -4)(x^4+4)

Again rewriting the first parentheses

5x^2 ( x^2 ^2 -2^2)(x^4+4)

5x^2 ( x^2 -2)(x^2 +2)(x^4+4)

The last term can be rewritten as(x^2+2x+2)(x^2-2x+2)

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

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