Question

$(x-5y{)}^3=$?

• A. $x^3+125y^3-15x^{2}y+75x{y}^2$
• B. $x^3-125y^3-15x^{2}y+75x{y}^2$
• C. $x^3+125y^3+10x^{2}y+75x{y}^2$
• D. None of the above

Answer 1

The correct option is B $x^3-125y^3-15x^{2}y+75x{y}^2$

We know, $(a-b{)}^3=a^3-b^3-3ab(a-b)$

and $(a-b{)}^3=a^3-b^3-3a^{2}b+3a{b}^2$

Then,

$(x-5y{)}^3$
$=(x{)}^3-(5y{)}^3-3\left(x{)}^2\right(5y)+3(x\left)\right(5y{)}^2$

$=x^3-125y^3-3\left(x^2\right)\left(5y\right)+3\left(x\right)\left(25y^2\right)$
$=x^3-125y^3-15x^{2}y+75x{y}^2$

Therefore, option $B$ is correct.