How do you factor #v^ { 4} + 16v ^ { 2} d ^ { 2} + 64d ^ { 4}#?

2 Answers
Cem Sentin
Dec 5, 2017

#(v^2+8d^2)^2#

Explanation:

#v^4+16v^2d^2+64d^4#

=#(v^2+8d^2)^2#

Alvin L.
Dec 5, 2017

#(v^2+8d^2)^2#

Explanation:

We can recognize that the expression is in the form of the expansion of #(a+b)^2#:
#(a+b)^2=a^2+2ab+b^2#

We can therefor tell that #a^2=v^4# and #b^2=64d^4#. Taking the square root of both of these equations, we get:
#a=v^2#, #b=8d^2# (Note that we're only interested in the positive square root, since the middle coefficient is positive).

This is all we need to know to be able to factor like so:
#v^4+16v^2d^2+64d^4=(v^2+8d^2)^2#

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