Expand and simplify the expression (x+5)(x+8).
This question is about multiplying two brackets together. There are two parts to each bracket: x, +3 and x, +5. The parts in the first bracket must each be multiplied by both parts in the second bracket. We use the claw method for this. We will draw lines, that each represent a multiplication. Draw a line from the first x to the second x (see whiteboard diagram). This means x times x, which is x2 so we write x2 as the first part of our answer. Now draw a line from the first x, to the "+8". Every line means a mutliplication so this means +8 times x, which we write as +8x next to our x2. Now we draw two lines from the +5 to the parts in the second bracket (as shown in diagram, you can see why it is called the claw method now!). The first is +5 times x, so +5x, followed by +5 times +8, which is +40. Now we have all parts to our answer: x2 +8x +5x +40. However we are not quite finished! We must simplify the expression, so write it with less parts to it! We can only simplify bits that look similar. So here the +8x and +5x are both numbers with an x attached to them. +8x means we have 8 x's and +5x means we have 5 x's. 8 + 5 = 13, so in total we have 13 x's, which we can write as +13x. So if we put this in our final answer, we get: x2 +13x +40. This is the correct answer.
