Question

1º - Responda (produtos notáveis)
a) (x+1/2)^2
b) 2m+n/2)^2
c) (x+5)^2 - (x-5)^2
d) a/3 - c/2)^2
e) 1/2 [(x+1)^2 + (x-1)^2]

Answer 1

$a) \ (x+\frac{1}{2})^2=x^2+x+\frac{1}{4}\\ \\ b) \ (2m+\frac{n}{2})^2=4m^2+mn+\frac{n^2}{4}\\ \\ c) \ (x+5)^2-(x-5)^2=x^2+10x+25-x^2+10x-25=20x\\ \\ d)(\frac{a}{3}-\frac{c}{2})^2=\frac{a^2}{9}-\frac{ac}{3}+\frac{c^2}{4}\\ \\ e)\frac{1}{2}[(x^1)^2+(x-1)^2]=\frac{1}{2}[x^2+2x+1+x^2-2x+1]=x^2+1$