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alina1380 [7]
3 years ago
8

What is the factored form of the binomial expansion x4 – 16x3 + 96x2 – 256x + 256?

Mathematics
1 answer:
navik [9.2K]3 years ago
7 0

Answer:

<h2>(x-4)*(x-4)*(x-4)*(x-4) or (x-4)^4</h2>

Step-by-step explanation:

x^4 – 16x^3 + 96x^2 – 256x + 256

terms with odd exponents are negative

x^4 has a coefficient of one, so the expression's GCF is 1

Thus, we need to factor out the expression as it is:

(x-4)*(x-4)*(x-4)*(x-4)

Lets multiply it out to check:

(x-4)*(x-4)*(x-4)*(x-4)=

(x^2-8x+16)*(x^2-8x+16)=

x^4−<em>8x^3</em>+<u>16x^2</u>−8x^3+<u>64x^2</u>−<em>128x</em>+<u>16x^2</u>−<em>128x</em>+<u><em>256</em></u>=

x^4 – 16x^3 + 96x^2 – 256x + 256

thus, the factored form is:

(x-4)*(x-4)*(x-4)*(x-4) or (x-4)^4

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