Mutiplying Brackets

2(x+2) means multiply x+2 by 2 + 4 2 × x = 2x 2 × 2 = 4 4(x-3) = 4x - 12 4 × x = 4x 4 × -3 = -12 -5(x-6) = -5x + 30 -5 × x = -5x -5 × -6 = +30

3(x - 4) + 2(x - 3) = 3x - 12 +2x - 6 = 5x - 18 3(2x - 4) - 2(x + 5) = 6x - 12 -2x - 10 = 4x - 22

Expand and simplify 1) 4(x + 2) 2) 5(x + 7) 3) 6(x + 8) 4) 3(3x + 4) 5) 5(6x + 1) 6) 3(5x + 2) 7) –2(x + 3) 8) –4(x + 2) 9) –6(x + 7) 10) 5(x – 7) 11) 3(x – 4) 12) 7(x – 5) 13) –5(x – 2) 14) –3(x – 3) 15) –4(x – 1) 16) –6(2x – 5) 17) –4(x – 2) 18) –2(x – 3) 19) –4(–3x + 3) 20) –7(–5x – 6) 1) 3(x + 3) + 4(x + 2) 2) 6(x + 4) – 2(x + 3) 3) 5(x + 3) + 2(x – 4) 4) 5(x + 3) + 4(x – 2) 5) 5(x – 4) + 3(x – 5) 6) 7(x – 4) – 4(x + 9) 7) 2(2x – 4) – 6(x + 3) 8) 5(3x + 6) – 4(x – 4) 9) –5(3x + 5) – 2(2x + 3) 10) 6(x + 2) – 3(3x – 5)

Multiplying brackets containing x terms 5×5 = 52 3 × 3 × 3 = 33 Using algebra x × x = x2 x × x × x = x3 2 × x × x = 2x2 2x × 3x = 6x2 2 × 3 = 6 x × x = x2

To Multiply 2 brackets use F O I L F O I L means multiply First by First Outer by Outer Inner by Inner Last by Last (x + 1) (x + 2) = x2 + 2x + 1x + 2 Last by Last Inner by Inner First by First Outer by Outer = x2 + 3x +2 x2 – 3x + 1x – 3 First by First Inner by Inner Outer by Outer Last by Last (x + 1) (x – 3) = = x2 – 2x – 3 (x – 2) (x – 3) = x2 – 3x – 2x + 6 = x2 – 5x + 6

First by First Outer by Outer Inner by Inner Last by Last (2x – 1)(x + 3) = 2x2 + 6x – x – 3 = 2x2 + 5x – 3 (2x – 1)(3x – 4) = 6x2 – 8x – 3x + 4 = 6x2 – 11x + 4 (2x – 1)2 means (2x – 1) (2x – 1) (2x – 1)(2x – 1) = 4x2 – 2x – 2x + 1 = 4x2 – 4x + 1

1) (x + 3)(x + 2) 2) (x + 4)(x + 3) 3) (x + 3)(x – 4)