Expand the following brackets: a) 4(x+3) b) 3(x-1)-2(x+5) c) (y-3)^2 d) (y-2)^2 + (y+3)^2

a) 4x + 12For this question you must expand out the bracket by multiplying the subjects within by the number at the front. 4x + (4 x 3) = 4x + 12
b) x - 13Although this question looks more confusing, you should simply use the same approach as a). Don't over complicate it by trying to do the additions in your head. I would recommend expanding the whole question before you attempt to simplify.3x - 3 - 2x - 10 (remember that a minus x plus = minus) = x - 13
c) y² - 6y + 9This question requires you to multiply two brackets together. First re-write as: (y - 3)(y - 3) and then expand. You do this through multiplying each term in one bracket with the ones in the other. For example, if we re-wrote it as: (a - b)(c - d) the general formula would be: ac - ad - bc + bdTherefore:y² - 3y - 3y + 9 = y² - 6y + 9
d) 2y² + 2y + 13For this question you should use the same approach as c: Expand and simplify(y - 2)(y - 2) + (y + 3)(y + 3) = (y² - 2y - 2y + 4) + (y² + 3y + 3y + 9) = 2y² - 4y + 6y + 13 = 2y² + 2y + 13