How do you factor completely #a^4-b^4 #?

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1 Answer
ProfLayton
Apr 19, 2016

#=(a^2+b^2)(a+b)(a-b)#

Explanation:

In algebra, there is a formula known as the Difference of two squares: #(a^2-b^2)=(a+b)(a-b)#

In the case of #a^4-b^4#, you'll see that #a^4# is just #(a^2)^2# and #b^4# is just #(b^2)^2#:
#a^4-b^4=(a^2)^2-(b^2)^2#
#=(a^2+b^2)(a^2-b^2)#
But as you can see, we can use the formula again:
#=(a^2+b^2)(a+b)(a-b)#
And this is the final answer

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