Question

QUESTAO 12
Calcule:
White
a) (5x - 1). (5x + 1) =

b) (a + b). (a + b) =

c) (2x² - 3X - 6)· ( 5x – 20 =

d) (2a + 3b). (a - b) =
​

Answer 1

Aplicando a propriedade distributiva:

a)

$(5x-1)~.~(5x+1)~=~(5x~.~5x)~+~(5x~.~1)~-~(1~.~5x)~-~(1~.~1)\\\\\\(5x-1)~.~(5x+1)~=~(25x^2)~+~(5x)~-~(5x)~-~(1)\\\\\\(5x-1)~.~(5x+1)~=~25x^2+5x-5x-1\\\\\\\boxed{(5x-1)~.~(5x+1)~=~25x^2-1}$

b)

$(a+b)~.~(a+b)~=~(a~.~a)~+~(a~.~b)~+~(b~.~a)~+~(b~.~b)\\\\\\(a+b)~.~(a+b)~=~(a^2)~+~(ab)~+~(ab)~+~(b^2)\\\\\\(a+b)~.~(a+b)~=~a^2+ab+ab+b^2\\\\\\\boxed{(a+b)~.~(a+b)~=~a^2+2ab+b^2}$

c)

$(2x^2-3x-6)~.~(5x-20)~=\\\\\\=~(2x^2~.~5x)~-~(2x^2~.~20)~-~(3x~.~5x)~+~(3x~.~20)~-~(6~.~5x)~+~(6~.~20)\\\\\\=~(10x^3)~-~(40x^2)~-~(15x^2)~+~(60x)~-~(30x)~+~(120)\\\\\\=~10x^3-40x^2-15x^2+60x-30x+120\\\\\\=~\boxed{10x^3-55x^2+30x+120}$

d)

$(2a+3b)~.~(a-b)~=~(2a~.~a)~-~(2a~.~b)~+~(3b~.~2a)~-~(3b~.~b)\\\\\\(2a+3b)~.~(a-b)~=~(2a^2)~-~(2ab)~+~(6ab)~-~(3b^2)\\\\\\(2a+3b)~.~(a-b)~=~2a^2-2ab+6ab-3b^2\\\\\\\boxed{(2a+3b)~.~(a-b)~=~2a^2+4ab-3b^2}$