Reminder: Removing Brackets Multiplying Pairs of Brackets

Reminder: Removing Brackets 2(a + 3) = 2a 2 × a 2 ×

Reminder: Removing Brackets 3(b - 4) = 3b 3 × b 3 ×

Reminder: Removing Brackets -4(c + 2) = -4c -4 × c -4 ×

But the area will also equal the total area of the smaller rectangles. A = (x + 3)(x + 2) A = (x + 3)(x + 2) (x + 3) (x + 2) Calculating Areas x 2x 3xx2x2 3 2 x 6 The diagram opposite shows a large rectangle made up from smaller rectangles. The area of the large rectangle will be equal to its length×breadth. A = A = x 2 + 5x Giving: Simplify:

(x + 2) Another Approach (x + 3) x 3 2 x Instead of using four smaller areas, we could use two: A = A = x 2 + 2x + 3x + 6 A = x 2 + 5x + 6 3(x + 2)x(x + 2) +

Another Approach (x + 2) 3x A = (x + 3)(x + 2) So now we can see that A = x(x + 2) + 3(x + 2) A = x 2 + 2x + 3x + 6 A = x 2 + 5x + 6 (x + 3) x 2

Example (x + 3) 4x A = (x + 4)(x + 3) Follow a similar method to find the larger area. A = x(x + 3) + 4(x + 3) A = x 2 + 3x + 4x + 12 A = x 2 + 7x + 12 (x + 4) x 3 Solution:

(x + 3) Multiplying Pairs of Brackets (x + 2)(x + 3) (x)2+ = = x 2 + 3x + 2x + 6 = x 2 + 5x + 6

(y - 3) Multiplying Pairs of Brackets (y + 4)(y - 3) (y)4+ = = y 2 – 3y + 4y - 12 = y 2 + y - 12

(z + 1) Multiplying Pairs of Brackets (z - 5)(z + 1) (z)5- = = z 2 + z – 5z - 5 = z 2 – 4z - 5