Factorise : 4 x^{2}+4 x y-3 y^{2} | vedclass

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(B) To factorise the quadratic expression $4 x^{2}+4 x y-3 y^{2}$,we use the splitting the middle term method.We need to find two numbers whose produc

Vedclass · Accepted Answer

$(2x + 3y)(2x - y)$

Vedclass · Answer

(B) To factorise the quadratic expression $4 x^{2}+4 x y-3 y^{2}$,we use the splitting the middle term method.We need to find two numbers whose product is $(4) 	imes (-3) = -12$ and whose sum is $4$.These two numbers are $6$ and $-2$.Now,rewrite the middle term $4xy$ as $6xy - 2xy$:$4 x^{2}+6 x y-2 x y-3 y^{2}$Group the terms:$= (4 x^{2}+6 x y) - (2 x y+3 y^{2})$Factor out the common terms from each group:$= 2 x(2 x+3 y)-y(2 x+3 y)$Finally,factor out the common binomial $(2 x+3 y)$:$= (2 x+3 y)(2 x-y)$

Factorise $: 4 x^{2}+4 x y-3 y^{2}$

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