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 +
3a + 2. This is your final answer.
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 +
3a + 2. This is your final answer.
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)

Answers
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