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Factorize: 4(x-y)^2-12(x-y)(x+y)+9(x+y)...

Factorize: `4(x-y)^2-12(x-y)(x+y)+9(x+y)^2`

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`4(x-y)^2-12(x-y)(x+y)+9(x+y)^2`
Let `(x-y)=a`,`(x+y)=b`
`=4a^2-2ab+9b^2`
By using middle term splitting:
`=4a^2-6ab-6ab+9b^2`
`=2a(2a-3b)-3b(2a-3b)`
`=(2a-3b)(2a-3b)`
`=(2a-3b)^2`
Substituting `a=x-y` and `b=x+y`
`=[2(x-y)-3(x+y)]`
`=[2x-2y-3x-3y]^2`
`=[2x-3x-2y-3y]^2`
`=[-x-5y]^2`
`=[(-1)(x+5y)]^2`
`=(1)(x+5y)^2`
`=(x+5y)^2`
`therefore 4(x-y)^2-12(x-y)(x+y)+9(x+y)^2=(x+5y)^2`
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