Question

. . Multiply: (x + 2y – z)(x2+ 4y2+z2 − 2xy+xz+ 2yz)

Answer 1

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

To find: Multiply the given expression.

Solution:

• Now we have given:

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

• Expanding it, we get:

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

• Now multiplying it, we get:

                x^3 + 4xy^2 + xz^2 - 2x^2y + x^2z + 2xyz + 2x^2y + 8y^3 + 2yz^2 - 4xy^2 + 2xyz + 4y^2z - x^2z - 4y^2z - z^3 + 2xyz - xz^2 - 2yz^2

• So after cancelling same terms, we get:

                x^3 +  8y^3 - z^3 + 6xyz

Answer:

              So the product of the given term is x^3 +  8y^3 - z^3 + 6xyz.