Past papers › WAEC · 2024 · May/June · General Maths · Paper 1 › Question 28 Question WAEC General Maths 2024 Objective Quadratics & their graphs Expressions, formulae & change of subject Quadratics & their graphs, Expressions, formulae & change of subject
WAEC 2024 · Paper 1 · Q28 Factorize completely: 27 x 2 − 48 y 2 27x^2 - 48y^2 27 x 2 − 48 y 2
A 3 ( 3 x + 4 y ) ( 3 x + 4 y ) 3(3x + 4y)(3x + 4y) 3 ( 3 x + 4 y ) ( 3 x + 4 y ) B 3 ( 3 x + 4 y ) ( 3 x − 4 y ) 3(3x + 4y)(3x - 4y) 3 ( 3 x + 4 y ) ( 3 x − 4 y ) C 3 ( 9 x − 16 y ) ( 9 x + 16 y ) 3(9x - 16y)(9x + 16y) 3 ( 9 x − 16 y ) ( 9 x + 16 y ) D 3 ( 9 x − 16 y ) ( 9 x − 16 y ) 3(9x - 16y)(9x - 16y) 3 ( 9 x − 16 y ) ( 9 x − 16 y )
Worked solution (try it first) Take out the common factor 3:
27 x 2 − 48 y 2 = 3 ( 9 x 2 − 16 y 2 ) 27x^2 - 48y^2 = 3(9x^2 - 16y^2) 27 x 2 − 48 y 2 = 3 ( 9 x 2 − 16 y 2 ) .
The bracket is a difference of two squares:
9 x 2 = ( 3 x ) 2 9x^2 = (3x)^2 9 x 2 = ( 3 x ) 2 and
16 y 2 = ( 4 y ) 2 16y^2 = (4y)^2 16 y 2 = ( 4 y ) 2 .
So
27 x 2 − 48 y 2 = 3 ( 3 x + 4 y ) ( 3 x − 4 y ) 27x^2 - 48y^2 = 3(3x + 4y)(3x - 4y) 27 x 2 − 48 y 2 = 3 ( 3 x + 4 y ) ( 3 x − 4 y ) , option B.
Watch out
Take square roots: 9 x 2 = 3 x \sqrt{9x^2} = 3x 9 x 2 = 3 x 16 y 2 = 4 y \sqrt{16y^2} = 4y 16 y 2 = 4 y 9 x 9x 9 x 16 y 16y 16 y 81 x 2 81x^2 81 x 2 256 y 2 256y^2 256 y 2 Report a problem with this question