Factorise 9 x^{2}-21 x y+10 y^{2}. | vedclass

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Question

(A) To factorise the quadratic expression $9 x^{2}-21 x y+10 y^{2}$,we use the splitting the middle term method.We need to find two numbers whose prod

Vedclass · Accepted Answer

$(3 x-2 y)(3 x-5 y)$

Vedclass · Answer

(A) To factorise the quadratic expression $9 x^{2}-21 x y+10 y^{2}$,we use the splitting the middle term method.We need to find two numbers whose product is $9 	imes 10 = 90$ and whose sum is $-21$.The two numbers are $-15$ and $-6$,since $(-15) 	imes (-6) = 90$ and $(-15) + (-6) = -21$.Now,rewrite the middle term $-21 x y$ as $-15 x y - 6 x y$:$9 x^{2} - 15 x y - 6 x y + 10 y^{2}$Group the terms:$(9 x^{2} - 15 x y) - (6 x y - 10 y^{2})$Factor out the common terms from each group:$3 x(3 x - 5 y) - 2 y(3 x - 5 y)$Finally,factor out the common binomial $(3 x - 5 y)$:$(3 x - 5 y)(3 x - 2 y)$

Factorise $9 x^{2}-21 x y+10 y^{2}$.

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