Past papers › WAEC · 2024 · May/June · General Maths · Paper 1 › Question 5 Question WAEC General Maths 2024 Objective Expressions, formulae & change of subject Quadratics & their graphs Expressions, formulae & change of subject, Quadratics & their graphs
Simplify: ( 2 p − q ) 2 − ( p + q ) 2 (2p - q)^2 - (p + q)^2 ( 2 p − q ) 2 − ( p + q ) 2
A 3 p ( p − 2 q ) 3p(p - 2q) 3 p ( p − 2 q ) B 2 p ( p − 3 q ) 2p(p - 3q) 2 p ( p − 3 q ) C 3 p ( 2 p − q ) 3p(2p - q) 3 p ( 2 p − q ) D 2 p ( 3 p − q ) 2p(3p - q) 2 p ( 3 p − q )
Worked solution (try it first) Use the difference of two squares,
A 2 − B 2 = ( A − B ) ( A + B ) A^2 - B^2 = (A - B)(A + B) A 2 − B 2 = ( A − B ) ( A + B ) , with
A = 2 p − q A = 2p - q A = 2 p − q and
B = p + q B = p + q B = p + q .
A − B = 2 p − q − p − q = p − 2 q A - B = 2p - q - p - q = p - 2q A − B = 2 p − q − p − q = p − 2 q , and
A + B = 3 p A + B = 3p A + B = 3 p .
So the expression is
3 p ( p − 2 q ) 3p(p - 2q) 3 p ( p − 2 q ) , option A.
Watch out
Subtract the whole of B B B ( 2 p − q ) − ( p + q ) = p − 2 q (2p - q) - (p + q) = p - 2q ( 2 p − q ) − ( p + q ) = p − 2 q q q q p p p 3 p 2 3p^2 3 p 2 Report a problem with this question