Question

Multiply: x² + 4y² + z³ + 2xy + xz − 2yz   by x − 2y − z 

Answer 1

 The given expression is

x² + 4y² + z³ + 2xy + xz − 2yz  

We have to multiply the above expression by. `(x-2y -z)`

The required product is

`(x-2y-z)(x^2 +4y^2 +z^2+2xy+ xz - 2yz)`

` = {x + (-2y)+(-z)}{(x)^2 +(-2y)^2 + (-z)^2 -x.(-2y) - (-2y).(-z) - (-z).x}`

Recall the formula

`a^3 +b^3 +c^3 -3abc = (a+b+c)(a^2 +b^2 +c^2 - ab - bc - ca)`

Using the above formula, we have

` = x^3 + ( -2y)^3 + (-z)^3 -3.x.(-2y).(-z)`

` = x^3 -8y^3 - z^3 - 6xyz`