Resolve into factors: 16(x-y)^{2}-9(x+y)^{2} | vedclass

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(C) Given expression: $16(x-y)^{2}-9(x+y)^{2}$This is in the form of $a^{2}-b^{2}$,where $a^{2} = 16(x-y)^{2} \implies a = 4(x-y)$ and $b^{2} = 9(x+y)

Vedclass · Accepted Answer

$(x-7y)(7x-y)$

Vedclass · Answer

(C) Given expression: $16(x-y)^{2}-9(x+y)^{2}$This is in the form of $a^{2}-b^{2}$,where $a^{2} = 16(x-y)^{2} \implies a = 4(x-y)$ and $b^{2} = 9(x+y)^{2} \implies b = 3(x+y)$.Using the identity $a^{2}-b^{2} = (a-b)(a+b)$:$= [4(x-y)-3(x+y)][4(x-y)+3(x+y)]$$= (4x-4y-3x-3y)(4x-4y+3x+3y)$$= (x-7y)(7x-y)$

Resolve into factors: $16(x-y)^{2}-9(x+y)^{2}$

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