Question

Fatore os seguintes polinômios usando diferença de quadrados

Answer 1

$\large\begin{array}{lr}\rm g)~~ \dfrac{1}{9} - 4y^2 \\\\\rm \left(\dfrac{1}{3}\right)^2 - (2y)^2 \\\\\rm \left(\dfrac{1}{3} + 2y\right)\left(\dfrac{1}{3} - 2y\right) \\\\\red{\underline{\boxed{\boxed{\rm \therefore\:\dfrac{1}{9} - 4y^2 = \left(\dfrac{1}{3} + 2y \right) \left(\dfrac{1}{3} - 2y \right) }}}}\end{array}$

 

$\large\begin{array}{lr}\rm h)~~ \dfrac{1}{25} - \dfrac{a^2}{16}\\\\\rm \left( \dfrac{1}{5} \right)^2 - \left( \dfrac{a}{4} \right)^2 \\\\\rm \left( \dfrac{1}{5} -\dfrac{a}{4} \right) \left( \dfrac{1}{5} + \dfrac{a}{4} \right) \\\\\red{\underline{\boxed{\boxed{\rm \therefore\: \dfrac{1}{25} - \dfrac{a^2}{16}= \left( \dfrac{1}{5} -\dfrac{a}{4} \right) \left( \dfrac{1}{5} + \dfrac{a}{4} \right) }}}}\end{array}$