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**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