Question

Multiply: x² + y² + z² − xy + xz + yz by x + y − z

Answer 1

The given expression is

 `x^2 +y^2 +z^2 - xy +xz + yz`

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

The required product is

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

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

` = x^3 +y^3 - z^3 +3xyz`