Question

Factorize the following using appropriate identities:
(i)$9x^2+6xy+y^2$
(ii)$4y^2-4y+1$
(iii)$x^2-\frac{y^2}{100}$

Answer 1

$\left(i\right)9x^2+6xy+y^2={\left(3x\right)}^2+2\times 3x\times y+{\left(y\right)}^2$ using $a^2+2ab+b^2={(a+b)}^2$

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

$\left(ii\right)4y^2-4y+1={\left(2y\right)}^2-2\times 2y\times 1+1^2$ using $a^2=2ab+b^2={(a+b)}^2$

$={(2y-1)}^2$

$\left(iii\right)x^2-\frac{y^2}{100}=x^2-\frac{y^2}{{10}^2}$ is of the form $a^2-b^2=(a+b)(a-b)$

$=(x+\frac{y}{10})(x-\frac{y}{10})$