Mathematics 2008 JAMB Past Questions - Question 14: Factorize completely (4x+3y)2 (3x-2y)2

Correct Answer

A

Explanation

(4x - 4k - 2y) (4x + 3y - 2y)To factorize completely the expression (4x + 3y)^2 (3x - 2y)^2, we can use the formula for factoring the square of a binomial, which is (a + b)^2 = a^2 + 2ab + b^2.Applying this formula to each binomial, we have:(4x + 3y)^2 = (4x)^2 + 2(4x)(3y) + (3y)^2            = 16x^2 + 24xy + 9y^2(3x - 2y)^2 = (3x)^2 - 2(3x)(2y) + (2y)^2            = 9x^2 - 12xy + 4y^2Now, we can multiply these two expressions together:(16x^2 + 24xy + 9y^2)(9x^2 - 12xy + 4y^2)To factorize completely, we can look for common factors and use the distributive property to simplify the expression further. However, in this case, there are no common factors that can be factored out, so the expression remains as:(16x^2 + 24xy + 9y^2)(9x^2 - 12xy + 4y^2)Therefore, the expression (4x + 3y)^2 (3x - 2y)^2 is already fully factorized.