How do you multiply $(-bc+a^2)(bc+a^2)$ ?

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Answer 1 · 2015-04-06T21:26:31

$a^4-b^2c^2$

Let's switch the terms around in the binomials:
$(a^2+bc)(a^2-bc)$
This is a difference of squares where:
$(x^2-y^2) = (x+y)(x-y)$

If we let $x=a^2$ and $y=bc$
$((a^2)^2-(bc)^2) = (a^2+bc)(a^2-bc)$

How do you multiply (-bc+a^2)(bc+a^2)(-bc+a^2)(bc+a^2)?