Question 1026660
<pre>
{{{8x^2-2y^2}}}

First we can take out a common factor of 2:

{{{2(4x^2-y^2)}}}

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We learn the principle of factorising the 
difference of two squares. Here 
is why it works:

A²-B² = (A-B)(A+B)

Proof: (A-B)(A+B) = A²+AB-AB-B² = A²-B²

So we memorise:

A²-B² is factorized as (A-B)(A+B)

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Now back to this:

{{{2(4x^2-y^2)}}}

Since 4=2², we can rewrite that as

{{{2(2^2x^2-y^2)}}}

and again as

{{{2((2x)^2-y^2)}}}

Since we have memorized that

A²-B² is factorised as (A-B)(A+B)

We can substitute 2x for A and y for B and get that

{{{2((2x)^2-y^2))}}} is factorised as {{{2(2x-y)(2x+y)}}}

Edwin</pre>