Question

Desenvolva esses quadrados
a) (x+1/2)²

b) (x-0,1)²

c) (0,5+x)²

d) (1/3-x)²

Answer 1

Produto Notável -----> O quadrado do 1° mais duas vezes o 1° multiplicado pelo 2° mais o quadrado do 2°.


$a)~~\left(x+ \dfrac{1}{2} \right)^2\to~~\left(x+ \dfrac{1}{2} \right) \left(x+ \dfrac{1}{2} \right)\to~~ x^2+ \dfrac{1}{2}x+ \dfrac{1}{2}x+ \dfrac{1}{4}\to\\\\\\ x^2+ 2.\left(\dfrac{1}{2}x\right)+ \dfrac{1}{4}\to~~x^2+ \dfrac{2}{2} x+ \dfrac{1}{4} \to~~ \large\boxed{x^2+x+ \frac{1}{4} }$




$b) ~~(x-0,1)^2\to~~ (x-0,1)(x-0,1)\to~~ x^2-0,1x-0,1x+0,01\to\\\\ \large\boxed{x^2-0,2x+0,01}\\\\\\\\\\ c) ~~(0,5+x)^2\to~~ (0,5+x)(0,5+x)\to~~ 0,25+0,5x+0,5x+x^2\to\\\\ 0,25+1x+x^2\to~~ \large\boxed{x^2+x+0,25}$




$d)~~\left( \dfrac{1}{3}-x \right)^2\to~~\left( \dfrac{1}{3}-x \right) \left( \dfrac{1}{3}-x \right)\to~~ \dfrac{1}{9}-\dfrac{1}{3}x-\dfrac{1}{3}x+x^2\to\\\\\\ \dfrac{1}{9}+2.\left(-\dfrac{1}{3}x\right)+x^2\to~~\dfrac{1}{9}-\dfrac{2}{3}x+x^2\to~~\large\boxed{x^2-\dfrac{2}{3}x+\dfrac{1}{9} }$