Factorize: x + y - ax = ay

Analyze the question: The question says "Factorize: x + y - ax = ay". The "= ay" looks like a typo. The original WASSCE question is most likely "Factorize x + y - ax - ay", and the "=" sign was probably meant to be a minus sign.

Concept: Factorizing by grouping means collecting terms that share a common factor, then pulling that factor out.

Solution:

Take the expression as x + y - ax - ay.

1. Group the terms: (x + y) - (ax + ay)
2. Factor the second group: ax + ay = a(x + y)
3. So the expression becomes (x + y) - a(x + y)
4. Take out the common factor (x + y):

(x + y)(1 - a)

Check by expanding: (x + y)(1 - a) = x - ax + y - ay = x + y - ax - ay ✓

Note on the typo: If the question is read literally as the equation x + y - ax = ay, then moving ay to the left gives x + y - ax - ay = 0. That is the same expression, set equal to zero, and it factorizes to (x + y)(1 - a) = 0. So the factor is the same either way.

Answer: C. (x + y)(1 - a)

Tip: When you see four terms, try grouping them in pairs. If the brackets match after you factor each pair, you can pull out the common bracket. Always expand your answer to check it, because it takes only a few seconds and catches sign errors.