Question

Calcule
a)(a+b)^3
b)(1-2a)^3
c(2x+y)^3
d(4y-1)^3

Answer 1

$a) \ (a+b)^3=(a+b)(a+b)^2=a+b)(a^2+2ab+b^2)=\\ =a^3+3 a^2 b+3 a b^2+b^3\\ \\b) \ (1-2a)^3=(1-2a)(1-2a)^2=(1-2a)(1-4a+4a^2)=\\ =-8 a^3+12 a^2-6 a+1\\ \\c) \ (2x+y)^3=(2x+y)(2x+y)^2=(2x+y)(4x^2+4xy+y^2)=\\ =8 x^3+12 x^2 y+6 x y^2+y^3\\ \\d \ (4y-1)^3=(4y-1)(4y-1)^2=(4y-1)(16y^2-8y+1)=\\ =64 y^3-48 y^2+12 y-1$

Answer 2

Oie, Td Bom?!

a)

$= (a + b) {}^{3}$

$= a {}^{3} + 3a {}^{2} b + 3ab {}^{2} + b {}^{3}$

b)

$= (1 - 2a) {}^{3}$

$= 1 {}^{3} - 3 \: . \: 1 {}^{2} \: . \: 2a + 3 \: . \: 1 \: . \: (2a) {}^{2} - (2a) {}^{3}$

$= 1 - 6a + 12a {}^{3} - 8a {}^{3}$

$= - 8a {}^{3} + 12a {}^{2} - 6a + 1$

c)

$= (2x + y) {}^{3}$

$= (2x) {}^{3} + 3 \: . \: (2x) {}^{2} \: . \: y + 3 \: . \: 2xy {}^{2} + y {}^{3}$

$= 8x {}^{3} + 3 \: .\: 4x {}^{2} y + 6xy {}^{2} + y {}^{3}$

$= 8x {}^{3} + 12x {}^{2} y + 6xy {}^{2} + y {}^{3}$

d)

$= (4y - 1) {}^{3}$

$= (4y) {}^{3} - 3 \: . \: (4y) {}^{2} \: . \: 1 + 3 \: . \: 4y \: . \: 1 {}^{2} -1 {}^{3}$

$= 64y {}^{3} - 3 \: . \: 16y {}^{2} \: . \: 1 + 3 \: . \: 4y \: . \: 1 - 1$

$= 64y {}^{3} - 48y {}^{2} + 12y - 1$

Att. Makaveli1996