Question

Multiply x²+4y²+z²+2xy+xz-2yz by (-z+x-2y)

Answer 1

hope it will help you..

Answer 2

Answer:  The required multiplied expression is $(x^3-8y^3-z^3-6xyz).$

Step-by-step explanation:  We are given to multiply the following :

$(x^2+4y^2+z^2+2xy+xz-2yz)~~~\textup{by}~~~(-z+x-2y).$

We know the following formula :

$a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ac).$

Let, a = -z, b = x  and  c = -2y.

So, we get

$(a+b+c)(a^2+b^2+c^2-ab-bc-ca)\\\\=(-z+x-2y)\{(-z)^2+x^2+(-2y)^2-(-z)\times x-x\times (-2y)-(-2y)\times (-z)\}\\\\=(-z+x-2y)(z^2+x^2+4y^2++zx+2xy-2yz)\\\\=(-z)^3+x^3+(-2y)^3-3\times(-z)\times x\times (-2y)\\\\=-z^3+x^3+8y^3-6xyz=x^3-8y^3-z^3-6xyz.$

Thus, the required multiplied expression is $(x^3-8y^3-z^3-6xyz).$