Question

5) Qual das alternativas abaixo é o resultado da soma entre (x + a)³ e ( x – a)³ ? *

A) 2x³ + 6a²x

B) 2x³ + 3xa² – 2x³ – 3xa²

C) x³ – 3 x²a + 3a²x – a³

D) 4x³ + 6a²x

Answer 1

$\sf (x + a)^{3}$

$\sf (x + a)\cdot (x + a)\cdot (x + a)$

$\sf (x + a)\cdot {x}^{2} + ax + ax + {a}^{2}$

$\sf (x + a)\cdot {x}^{2} + 2ax + {a}^{2}$

$\sf {x}^{3} + 2a {x}^{2} + {a}^{2} x + {ax}^{2} + 2 {a}^{2} x + {a}^{3}$

$\sf {x}^{3} + 2ax^{2} + a {x}^{2} + {a}^{2}x + 2 {a}^{2} x + {a}^{3}$

$\sf {x}^{3} + 3 {ax}^{2}$

$\sf \sf {x}^{3} + 3 {ax}^{2} + 3 {a}^{2} x + {a}^{3}$

$\sf (x - a)^{3}$

$\sf (x - a)\cdot (x - a)\cdot (x - a)$

$\sf (x - a)\cdot ({x}^{2} - ax - ax + {a}^{2} )$

$\sf (x - a)\cdot ({x}^{2} - 2ax+ {a}^{2} )$

$\sf {x}^{3} - 2ax^{2} + a^{2}x - a {x}^{2} + 2 {a}^{2} x - {a}^{3}$

$\sf {x}^{3} - 2a {x}^{2} - a {x}^{2} + {a}^{2} x + 2 {a}^{2} x - {a}^{3}$

$\sf {x}^{3} - 3 {ax}^{2} + 3 {a}^{2} x - {a}^{3}$

Soma

$\sf {x}^{3} + 3 {ax}^{2} + 3 {a}^{2} x + {a}^{3} + {x}^{3} - 3 {ax}^{2} + 3 {a}^{2} x - {a}^{3}$

$\sf {x}^{3} + {x}^{3} + 3 {ax}^{2} - 3 {ax}^{2} + 3 {a}^{2} x + 3 {a}^{2} x + {a}^{3} - {a}^{3}$

$\red{\sf {2x}^{3} + 6 {a}^{2} x}$

$\boxed{\boxed{\sf Letra \: A}}$