BECE Mathematics 2011 Paper

Concept:Factorisation means rewriting an algebraic expression as a product of its factors by taking out common terms.Explanation:Group the terms to make the common factor visible.$b^2 + fb - mb - fm = (b^2 + fb) - (mb + fm)$Take $b$ common from the first group:$b^2 + fb = b(b + f)$Take $m$ common from the second group:$mb + fm = m(b + f)$So the whole expression becomes:$b(b + f) - m(b + f)$Now $(b + f)$ is common in both terms.Factor out $(b + f)$:$(b + f)(b - m)$Thus the complete factorised form is $(b+f)(b-m)$.Answer:Option B: $(b+f)(b-m)$