Question

Factorise the following:

x²yz + xyz² + xy²z

Answer 1

Given expression: x²yz + xyz² + xy²z

Step-wise calculation:

1. Identify the common factors in all terms:

Each term contains x, y and z.

The lowest powers of variables common in all terms are:

• x to the first power
• y to the first power
• z to the first power

2. Take out the common factor xyz:

x²yz + xyz² + xy²z = xyz × remaining terms

3. Divide each term by the common factor to find the remaining terms inside the bracket:

`(x^2yz)/(xyz) = x`,

`(xyz^2)/(xyz) = z`,

`(xy^2z)/(xyz) = y`,

4. So the expression becomes xyz(x + z + y).