Answer:
A) 5x²(x^(8) - 16)
B) 5x²[(x⁴ + √16) • (x² + ∜16) • (x + (8√16) • (x - (8√16))]
Step-by-step explanation:
We are given the expression;
5x^(10) - 80x²
A) Since the expression is, 5x^(10) - 80x², the greatest common factor is 5x². So we will factorize that out.
So, we have;
5x²(x^(8) - 16)
B) The complete factorization of 5x²(x^(8) - 16) will be;
5x²[(x⁴ + √16) • (x⁴ - √16)]
Now, (x⁴ - √16)] can be broken than further into;
(x² + ∜16) • (x² - ∜16)
Also, (x² - ∜16) can be broken down into;
[(x + (8√16) • (x - (8√16))
So, our complete factorization gives us;
5x²[(x⁴ + √16) • (x² + ∜16) • (x + (8√16) • (x - (8√16))]