How do I expand (x - 4)(2x + 3y)^2 ?

To start off, to make things clearer we can write the expression as:(x - 4)(2x + 3y)(2x + 3y)Now focus on just two of the brackets, say (2x + 3y)(2x + 3y). To expand this, we need to do the following four multiplications: the first term in the first bracket (2x) with the first term in the second bracket (2x) to get 4x^2, the first term in the first bracket (2x) with the second term in the second bracket (3y) to get 6xy, the second term in the first bracket (3y) with the first term in the second bracket (2x) to get 6xy and finally the second term in the first bracket (3y) with the second term in the second bracket (3y) to get 9y^2. The expansion of the expression is then the sum of all these terms: 4x^2 + 6xy + 6xy + 9y^2. We can simplify this immediately to get: (2x + 3y)(2x + 3y) = 4x^2 + 12xy + 9y^2.This means we now want to expand: (x - 4)(4x^2 + 12xy + 9y^2). We use the same technique as before, that is, to multiply each term in the first bracket with each term in the second bracket, then take the sum of these. Thus, we find the answer: 4x^3 + 12x^2y + 9xy^2 - 16x^2 - 48xy - 36y^2.