Question 221983
{{{2t^2y^4-32t^2}}} Start with the given expression



{{{2t^2(y^4-16)}}} Factor out the GCF {{{2t^2}}}



Now let's focus on the inner expression {{{y^4-16}}}


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{{{y^4-16}}} Start with the given expression.



{{{(y^2)^2-16}}} Rewrite {{{y^4}}} as {{{(y^2)^2}}}.



{{{(y^2)^2-(4)^2}}} Rewrite {{{16}}} as {{{(4)^2}}}.



Notice how we have a difference of squares. So let's use the difference of squares formula {{{A^2-B^2=(A+B)(A-B)}}} to factor the expression:



{{{(y^2+4)(y^2-4)}}} Factor the expression using the difference of squares.



You can then factor {{{y^2-4}}} further (using the difference of squares rule described above) to get {{{y^2-4=(y+2)(y-2)}}}



So {{{y^4-16}}} factors to {{{(y^2+4)(y+2)(y-2)}}}.



In other words {{{y^4-16=(y^2+4)(y+2)(y-2)}}}.

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So {{{2t^2(y^4-16)}}} then factors further to {{{2t^2(y^2+4)(y+2)(y-2)}}} 


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Answer:

So {{{2t^2y^4-32t^2}}} completely factors to {{{2t^2(y^2+4)(y+2)(y-2)}}} 



In other words, {{{2t^2y^4-32t^2=2t^2(y^2+4)(y+2)(y-2)}}}