Question

Factorise the following:

x(x + 2y – z) – 2yz

Answer 1

Given: x(x + 2y – z) – 2yz

Step-wise calculation:

1. Expand the first term:

x(x + 2y – z) = x² + 2xy – xz

2. Substitute back:

x² + 2xy – xz – 2yz

3. Group terms to factor by grouping:

x² + 2xy – (xz + 2yz)

4. Factor out common terms in the grouped parts:

From the first two terms:

x(x + 2y)

From the last two terms:

–z(x + 2y)

5. Take out the common factor (x + 2y):

(x + 2y)(x – z)