Question

Aplicando productos notables resuelvo los ejercicios

a. $(\frac{5}{3} x- \frac{6}{5}y)^{2}$
b. $(6x+2z)(5x-8z)$

Answer 1

$a)\left(\frac{5x}{3}-\frac{6y}{5}\right)^2$
${Aplicar\:la\:siguiente\:regla\:de\:productos\:notables}:$(a-b)²=a²-2ab+b²
$=\left(\frac{5x}{3}\right)^2-2\cdot \frac{5x}{3}\cdot \frac{6y}{5}+\left(\frac{6y}{5}\right)^2$
$=\frac{25x^2}{9}-4xy+\frac{36y^2}{25}$

$b)\left(6x+2z\right)\left(5x-8z\right)$
$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$
$a=6x,\:b=2z,\:c=5x,\:d=-8z$
$=6x\cdot \:5x-6x\cdot \:8z+2z\cdot \:5x-2z\cdot \:8z$
$=30x^2-38xz-16z^2$