Question

Find the cube of 3x - 2y - 4z

• A. $27x^3-54x^{2}y+36x{y}^2-8y^3-108x^{2}z+144xyz-48y^{2}z+144x{z}^2-96y{z}^2-64z^3$
• B. $81x^3-54x^{2}y+36x{y}^2-8y^3-108x^{2}z+144xyz-48y^{2}z+169x{z}^2-96y{z}^2-27z^3$
• C. $81x^3+54x^{2}y+36x{y}^2-8y^3-108x^{2}z+27xyz-48y^{2}z+169x{z}^2-96y{z}^2-27z^3$
• D. $27x^3+54x^{2}y+36x{y}^2+8y^3+108x^{2}z+144xyz-48y^{2}z+144x{z}^2-96y{z}^2-64z^3$

Answer 1

The correct option is A $27x^3-54x^{2}y+36x{y}^2-8y^3-108x^{2}z+144xyz-48y^{2}z+144x{z}^2-96y{z}^2-64z^3$

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

So if a=3x-2y and b=-4z we get

$(3x-2y{)}^3-12z(3x-2y{)}^2+48z^2(3x-2y)-64z^3$

$(3x-2y{)}^3=27x^3-54x^{2}y+36x{y}^2-8y^{3}and(3x-2y{)}^2=9x^2-12xy+4y^2$

$\therefore (3x-2y-4z{)}^3=27x^3-54x^{2}y+36x{y}^2-8y^3-108x^{2}z+144xyz-48y^{2}z+144x{z}^2-96y{z}^2-64z^3$.