EXPANDING DOUBLE BRACKETS

The area of a rectangle that has sides of length (x + 5) and (x + 2) can be found by splitting the rectangle into four parts. x + 5 x 2 5 x2 5x x + 2 2x 10 So

You can multiply double brackets without using a diagram. To expand double brackets you multiply each term in the first bracket by each term in the second bracket. Use the mnemonic FOIL to help you. F L F first O outside I inside L last I O

Solving problems

x + 7 1 The shaded area is 40 cm2. Find x. x x + 3 x rectangle – square = 40 expand the brackets simplify take 21 from both sides divide both sides by 10

2 Find x for this right angled triangle. 6 Use Pythagoras x expand the brackets take x2 from both sides take 1 from both sides divide both sides by 2

3 Write down and simplify an expression for the surface area of the cuboid. x + 2 x x + 5 surface area = sum of areas of the six faces expand the brackets simplify