Question

Factorise the following:

p²(q² + r²) + p(q² + r²) + (q² + r²)²

Answer 1

Given expression: p²(q² + r²) + p(q² + r²) + (q² + r²)²

Step 1: Identify the common factor in all the terms.

Here, each term has a factor of (q² + r²).

Step 2: Factor out (q² + r²):

p²(q² + r²) + p(q² + r²) + (q² + r²)² 

= (q² + r²)(p² + p + (q² + r²)

The factorised form is (q² + r²)(p² + p + q² + r²).