1a) Simplify 2a^3 x a^5 1b) (4x^2)^3 1c) 2(3y+1) - 3(y-4)

1a) To simplify this into one expression you first multiply together the co-efficients, therefore 2a x a = 2a. Then for indices when they are multiplied together you add them, so the simplification would be 2a^(3+5), leaving you with the answer of 2a^8                 1b) For this question you have to be careful to notice the position of the brackets. The easiest way to calculate the new term is to approach the '4' and 'x^2' parts of the bracket seperately and multiply them together at the end. So to begin with you do 4^3, which equals 64. Then you do (x^2)^3, which to work out you multiply the 2 and 3 together to get your indice for x. Therefore by multiplying both results together you get the final answer of 64x^6                                                                1c) In answering this question you want to treat both the expressions seperately, referred to here as A and B respectively. So for expanding the brackets on the first expression you multiply the terms inside the bracket by the value outside of it. So for expression A it would be (2 x 3y) + (2 x 1), giving the expanded expression of 6y +2. In Expression B the minus sign is very important in obtaining the right answer as it is used as part of the multiplying value outside the bracket. So you use the same method as in A, so you get (-3 x y) + (-3 x -4), giving you the expression of -3y +12, with the multiplication of double negative producing a positive value. Then you put both expressions together, so you get 6y + 2 - 3y + 12, leaving you with the answer of 3y + 14