Question

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

Answer 1

According to the question:

(x² + 4y² + z² + 2xy + xz – 2yz) × (–z + x – 2y)

Now, multiply as follows:

= {x + (–2y) + (–z)}{(x)² + (–2y)² + (–z²) – (x)(–2y) – (–2y)(–z) – (–z)(x)}

= x³ + (–2y)³ + (–z)³ – 3 × x × (–2y) × (–z)

Use the identity:

(a + b + c)(a² + b² + c² – ab – bc – ca) = a³ + b³ + c³ – 3abc

= x³ – 8y³ – z³ – 6xyz