Question

Factorise :
(i) (x + 2y)²– 9 (2x - y)²​

Answer 1

Answer:

-5(7x-y)(x-y)

Step-by-step explanation:

$(x+2y)^2 - 9(2x-y)^2\\= x^2 + 2(x)(2y) +(2y)^2 - 9[(2x)^2 - 2(2x)(y) + y^2]\\= x^2 + 4xy +4y^2 - 9[4x^2 - 4xy + y^2]\\= x^2 + 4xy +4y^2 -36x^2 + 36xy - 9y^2\\= -35x^2 +40xy - 5y^2\\= -5(7x^2-8xy+y^2)\\= -5(7x^2-7xy-xy+y^2)\\=-5[7x(x-y) -y(x-y)]\\=-5(7x-y)(x-y)$

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Answer 2

Step-by-step explanation:

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