Question

Utilizando as regras dos produtos notáveis, calcule:
a) (a4 +m4) (a4 + m4)
b) (a3 + 6y3)²
c) (m2 + 2n3)²
d) (bc + 1/3a) (bc - 1/3a)
e) (3ab + 1)²

Answer 1

Temos que:

$\mathsf{(a+b)^2=a^2+2ab+b^2}\\\\ \mathsf{(a-b)^2=a^2-2ab+b^2}\\\\ \mathsf{(a+b)(a-b)=a^2-b^2}$

Resolvendo:

a)

$\mathsf{(a^4+m^4)(a^4+m^4)}\\\\ \mathsf{(a^4+m^4)^2}\\\\ \boxed{\mathsf{a^8+2a^4m^4+m^8}}$


b)

$\mathsf{(a^3-6y^3)^2}\\\\ \boxed{\mathsf{a^6-12a^3b^3+36b^6}}$


c)

$\mathsf{(m^2+2n^3)^2}\\\\ \boxed{\mathsf{m^4+4m^2n^3+4n^6}}$


d)

$\mathsf{\left( bc+\dfrac{1}{3}a \right)\left( bc-\dfrac{1}{3}a\right) }\\\\\\ \boxed{\mathsf{b^2c^2-\dfrac{1}{9}a^2}}$


e)

$\mathsf{(3ab+1)^2}\\\\ \boxed{\mathsf{9a^2b^2+6ab+1}}$