Question

1 – Desenvolva os produtos notáveis:
a) (x – 5)²
b) (2x+y)²
c) ( − √)²

d) (√5 − √2)²

e) (x + 2)(x - 2)
f) (3² - b²)(3a² + b³)

Answer 1

a)
$(x - 5) {}^{2} = (x - 5)(x - 5) \\ = x {}^{2} - 5x - 5x + 25 \\ = x {}^{2} - 10x + 25$
b)
$(2x + y) {}^{2} = (2x + y)(2x + y) \\ = 4x {}^{2} + 2xy + 2xy + y {}^{2} \\ 4x {}^{2} + 4xy + y {}^{2}$
c)
$( - \sqrt{} ) {}^{2} = 1$

d)
$( \sqrt{5} - \sqrt{2} )( \sqrt{5} - \sqrt{2} ) \\ = 5 - \sqrt{10} - \sqrt{10} + 2 \\ = 7 - 2 \sqrt{10}$

e)
$(x + 2)(x - 2) \\ = x {}^{2} - 2x + 2x - 4 \\ = x {}^{2} - 4$

f)
$(3 {}^{2} - b {}^{2} )(3a {}^{2} + b { }^{3} ) \\ = 27a {}^{2} + 9b {}^{2} - 3a {}^{2} b {}^{2} - b {}^{5}$