Question

Produtos notáveis
A) (9x^2-1)^2
B) (X-5Y^3)^2
C) (X^3-M^3)^2
D)(X+1/2) (X-1/2)
E)(X-2/3) (X+2/3)
F)(X/4+2/3) (X/4-2/3)
me ajuda ai pessoal

Answer 1

a) $(9x^2-1)^2=(9x)^2-2\cdot9x^2\cdot1+1^2=81x^4-18x^2+1$

b) $(x-5y^3)^2=x^2-2\cdot x\cdot5y^3+(5y^3)^2=x^2-10xy^3+25y^6$

c) $(x^3-m^3)^2=(x^3)^2-2\cdot x^3\cdot m^3+(m^3)^2=x^6-2x^3m^3+m^6$

d) $\left(x+\dfrac{1}{2}\right)\left(x-\dfrac{1}{2}\right)=x^2-\left(\dfrac{1}{2}\right)^2=x^2-\dfrac{1}{4}$

e) $\left(x-\dfrac{2}{3}\right)\left(x+\dfrac{2}{3}\right)=x^2-\left(\dfrac{2}{3}\right)^2=x^2-\dfrac{4}{9}$

f) $\left(\dfrac{x}{4}+\dfrac{2}{3}\right)\left(\dfrac{x}{4}-\dfrac{2}{3}\right)=\left(\dfrac{x}{4}\right)^2-\left(\dfrac{2}{3}\right)^2=\dfrac{x^2}{16}-\dfrac{4}{9}$