Factorise the following $9 x^{2} + 6 x y + y^{2}$ .

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Solution

$9 x^{2} + 6 x y + y^{2}$
$(3 x)^{2} + 2 \times 3 x \times y + (y)^{2}$
this is ( $(a + b)^{2} = a^{2} + b^{2} + 2 a b$ )
$(3 x + y)^{2}$
The factorisation of $9 x^{2} + 6 x y + y^{2}$ is $(3 x + y)^{2}$

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