Question

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

Answer 1

Answer:

Multiply x

2 + 4y

2 + z

2 + 2xy + xz – 2yz by (– z + x – 2y).

The product of given polynomials is given by

(– z + x – 2y)(x

2 + 4y

2 + z

2 + 2xy + xz – 2yz)

= (x – 2y – z)(x

2 + 4y

2 + z

2 + 2xy – 2yz + xz)

= [(x) + (–2y) + (–z)][(x)

2 + (–2y)

2 + (–z)

2 – (x) (–2y) – (–2y) (–z) – (–z) (y)]

= (x)

3 + (–2y)

3 + (–z)

3 – 3(x)(–2y) (–z)

[∵ (a + b + c)(a

2 + b2+ c

2 – ab – bc – ca) = a

3 + b

3+ c

3 – 3abc]

= x

3 – 8y3 – z

3 – 6xyz