Question

Factorise
Q:- 9x^2+6xy+y^2

Answer 1

Rewrite 9x29x2 as (3x)2(3x)2.

(3x)2+6xy+y2(3x)2+6xy+y2

Check the middle term by multiplying 2ab2ab and compare this result with the middle term in the original expression.

2ab=2⋅(3x)⋅y2ab=2⋅(3x)⋅y

Simplify.

2ab=6xy2ab=6xy

Factor using the perfect squaretrinomial rule a2+2ab+b2=(a+b)2a2+2ab+b2=(a+b)2, where a=3xa=3x and b=yb=y.

(3x+y)2

Answer 2

$\huge\bf{Answer:-}$

given:-

$(a + b) {}^{2} = a {}^{2} = a {}^{2} + 2ab + b {}^{2}$

$(9x {}^{2} + 6xy + y {}^{2} )$

Also can be written as:-

$(3x) {}^{2} + 2(3x)y + (y) {}^{2}$

So,

$(3x) {}^{2} + 2(3x)y + (y) {}^{2}$

$(3x) {}^{2} + 2(3x)y + (y) {}^{2}$

Therefore,

$= (3x + y) {}^{2}$

Identity used here:-

$= a {}^{2} + 2ab + b {}^{2}$