# First – multiply the first term in each bracket together ### EXPANDING DOUBLE BRACKETS

Expanding Double Brackets

There are two methods that can be used to expand double brackets, both are shown here, use whichever you find easiest to remember.

E.g. Expand (a + 1)(a + 2)

This means we want to multiply everything in the first bracket by everything in the second bracket.

Method 1 – FOIL (Stands for First Outer Inner Last)

First – multiply the first term in each bracket together

Outer – multiply the outer term in each bracket together

Inner - multiply the inner term in each bracket together

Last - multiply the last term in each bracket together

Once these have all been multiplied, bring the terms together and simplify. The example simplifies to a 2 +

Method 2 – Using a Grid

Set up a 3x3 grid and put the terms from the first bracket down the side and the second bracket across the top as shown below: x a

+ 1 a + 2 x a a + 2 a 2 +2a

Multiply the terms together + 1 +a +2 in the grid

Once these have all been multiplied, bring the terms together and simplify. The example simplifies to a 2 +

RED

1.

(a+3)(a+5)

2.

(c+4)(c+8)

3.

(x+5)(x+5)

4.

(x+2)(x+9)

5.

(x+1)(x+1)

6.

(x +2)(x+4)

7.

(x+5)(x+2)

8.

(x+4)(x+5)

AMBER

1.

(a+3)(a-5)

2.

(c-4)(c+8)

3.

(x+5)(x-5)

4.

(x-2)(x+9)

5.

(x+1)(x-1)

6.

(x -2)(x+4)

7.

(x-5)(x+2)

8.

(x-4)(x+5)

GREEN

1.

(a-3)(a-5)

2.

(c-4)(c-8)

3.

(x-5)(x-5)

4.

(2x+2)(x+3)

5.

(x+1)(2x+1)

6.

(x +2)(2x+4)

7.

(2x+5)(x-2)

8.

(x-4)(2x+5)

RED

1.

(a+3)(a+5) a 2 +8a +15

2.

(c+4)(c+8) c 2 +12c +32

3.

(x+5)(x+5) x 2 +10x +25

4.

(x+2)(x+9) x 2 +11x +18

5.

(x+1)(x+1) x 2 +2x +1

6.

(x +2)(x+4) x 2 +6x +8

7.

(x+5)(x+2) x 2 +7x +10

8.

(x+4)(x+5) x 2 +9x +20

AMBER

1.

(a+3)(a-5) a 2 +-2a -15

2.

(c-4)(c+8) c 2 +4c -32

3.

(x+5)(x-5) x 2 - 25

4.

(x-2)(x+9) x 2 +7x -18

5.

(x+1)(x-1) x 2 -1

6.

(x -2)(x+4) x 2 +2x -8

7.

(x-5)(x+2) x 2 -3x -10

8.

(x-4)(x+5) x 2 +x -20

GREEN

1.

(a-3)(a-5) a 2 -8a +15

2.

(c-4)(c-8) c 2 -12c +32

3.

(x-5)(x-5) x 2 -10x +25

4.

(2x+2)(x+3)

2x 2 +8x +6

5.

(x+1)(2x+1)

2x 2 +3x +1

6.

(x +2)(2x+4)

2x 2 +8x +8

7.

(2x+5)(x-2)

2x 2 +x -10

8.

(x-4)(2x+5)

2x 2 -3x -20