Question

1) Resolva os produtos notáveis
a) (x + 1/2y)²
b) (4x + 2z)²
c) (9 - x) . (9 + x)
d) (3x - 5y)²
e) (2x - 3)²

Answer 1

Oie, tudo bom?

a)

$= (x + \frac{1}{2} y) {}^{2} \\ = x {}^{2} + 2x \: . \: \frac{1}{2} y + ( \frac{1}{2} y) {}^{2} \\ \boxed{ = x {}^{2} + xy + \frac{1}{4} y {}^{2} }$

b)

$= (4x + 2z) {}^{2} \\ = (4x) {}^{2} + 2 \: . \: 4x \: . \: 2z + (2z) {}^{2} \\ \boxed{ = 16x {}^{2} + 16xz + 4z {}^{2} }$

c)

$= (9 - x) \: . \: (9 + x) \\ = 9 {}^{2} - x {}^{2} \\ \boxed{ = 81 - x {}^{2} }$

d)

$= (3x - 5y) {}^{2} \\ = (3x) {}^{2} - 2 \: . \: 3x \: . \: 5y + (5y) {}^{2} \\ \boxed{ = 9x {}^{2} - 30xy + 25y {}^{2} }$

e)

$= (2x - 3) {}^{2} \\ = (2x) {}^{2} - 2 \: . \: 2x \: . \: 3 + 3 {}^{2} \\ \boxed{ = 4x {}^{2} - 12x + 9}$

Att. NLE Top Shotta