Question

10) Resolver os produtos notáveis abaixo:

Answer 1

$\large\boxed{\begin{array}{l}\rm a)~\sf(4x^2-3y)^2=(4x)^2-2\cdot4x^2\cdot3y+(3y)^2\\\sf (4x^2-3y)^2=16x^2-24x^2y+9y^2\\\rm b)~\sf(5ab-7)^2=( 5ab)^2-2\cdot5ab\cdot7+7^2\\\sf (5ab-7)^2=25a^2b^2-70ab+49\\\rm c)~\sf(11a^2b^3+7)^2=(11a^2b^3)^2+2\cdot11a^2b^3\cdot7+7^2\\\sf (11a^2b^3+7)^2=121a^4b^6+154a^2b^3+49\\\rm d)~\sf(m+5)^3=m^3+3\cdot m^2\cdot5+3\cdot m\cdot5^2+5^3\\\sf (m+5)^3=m^3+15m^2+75m+125\end{array}}$

$\large\boxed{\begin{array}{l}\rm e)~\sf(3x^2-4)\cdot(3x^2+4)=(3x^2)^2-4^2\\\sf (3x^2+4)^2=9x^4-16\\\rm f)~\sf (-t+8)^2=(8-t)^2=8^2-2\cdot8\cdot t+t^2\\\sf (8-t)^2=64-16t+t^2\end{array}}$

$\large\boxed{\begin{array}{l}\rm g)~\sf\bigg( \dfrac{x^2y^3}{z}+\dfrac{5}{6}\bigg)\cdot\bigg(\dfrac{x^2y^3}{z}-\dfrac{5}{6}\bigg)\\\\\sf=\bigg(\dfrac{x^2y^3}{z}\bigg)^2-\bigg(\dfrac{5}{6}\bigg)^2\\\\\sf=\dfrac{x^4y^6}{z^2}-\dfrac{25}{36}\end{array}}$