Question

Find the cube of $x+2y$.

• A. $x^3+8y^3+6x^{2}y+12x{y}^2$
• B. $x^3+8y^3+6x^{2}y-12x{y}^2$
• C. $x^3+8y^3+12x^{2}y+6x{y}^2$
• D. $x^3+8y^3-6x^{2}y+12x{y}^2$

Answer 1

The correct option is A

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

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

Using identity: $(a+b{)}^3=a^3+b^3+3a^{2}b+3a{b}^2$, we get

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

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