Question #3fdac

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Answer 1 · 2015-01-20T17:04:29

The key is to use powers to express your two terms.

Your first term can be written as $8 = 2^{3}$ $8 = 2^3$ , and your second term can be written as $z^{6} = {(z^{2})}^{3}$ $z^6 = (z^2)^3$ , which makes your expression

$2^{3} + {(z^{2})}^{3} = (2 + z^{2}) (2^{2} - 2 \cdot z^{2} + {(z^{2})}^{2})$ $2^3 + (z^2)^3 = (2 + z^2)(2^2 -2*z^2 + (z^2)^2)$

$2^{3} + {(z^{2})}^{3} = (2 + z^{2}) (4 - 2 z^{2} + z^{4})$ $2^3 + (z^2)^3 = (2 + z^2)(4 - 2z^2 + z^4)$

I've used the fact that

$a^{3} + b^{3} = (a + b) (a^{2} - a b + b^{2})$ $a^3 + b^3 = (a+b)(a^2 - ab + b^2)$

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Question #3fdac

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