Reminder Brackets Multiplying Removing Pairs of Brackets Reminder

Reminder: Brackets Multiplying. Removing Pairs of Brackets

Reminder: Removing Brackets 22 ×× a +3 2(a + 3) = 2 a + 6

Reminder: Removing Brackets 33 ×× b -4 3(b - 4) = 3 b - 12

Reminder: Removing Brackets -4 -4 × c× +2 -4(c + 2) = -4 c - 8

Calculating Areas 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. x Simplify: + 3 x 2 3 x (x + 2) 2 2 x 6 (x + 3) Giving: A = (x + 3)(x + 2) A = x + A = x 2 + 5 x + 6 + But the area will also equal the total area of the smaller rectangles.

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

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

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

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

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

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