Algebraic Expressions Algebraic Terms Examples 2 a means

Algebraic Expressions Algebraic Terms Examples 2 a means 2 a If p = 3, q = 4, r = 6 ab means a b 5 p = 5 3 = 15 a 2 means a a qr = 4 6 = 24 a 3 means a a a r 2 = 6 6 = 36 a b means a b p 3 = 3 3 3 = 27 a 2 b means c a a b c pq 3 4 12 =2 = = 6 6 r 6– 3 r–p = 34 = q 4

Adding and subtracting terms Examples 5 x – 4 y + 2 x + 6 y = 7 x + 2 y 5 x – 4 y + 2 x + 6 y 2 x 2 – x + 7 + x 2 – 4 x – 3 2 x 2 – x + 7 + x 2 – 4 x– 3 = 3 x 2 – 5 x + 4 a 2 + 3 ab – 4 b 2 + 2 a 2 – 5 ab – 7 b 2 = 3 a 2 – 2 ab – 11 b 2 a 2 + 3 ab – 4 b 2 + 2 a 2 – 5 ab – 7 b 2

Expanding a bracket Examples 3(2 x + 1) = 6 x + 3 3 2 x 3 1 a(a – b) = a 2 – ab a a a –b 4 p(3 p + 2 q – 5) = 12 p 2 + 8 pq – 20 p 4 p 3 p 4 p – 5 4 p 2 q

Expanding 2 brackets Examples (2 x – 3) (4 x + 5) = 8 x 2 + 10 x – 12 x – 15 = 8 x 2 – 2 x – 15 + 10 x – 12 x 2 x 4 x– 35 4 x – 3 5 5(x – 2 y) – 2(2 x – 3 y) = 5 x – 10 y – 4 x + 6 y = x – 4 y 5 x – 10 y– 4 x + 6 y 5 x 2 x – 2 – 3 y 5– 2 – 2 y 4 x(x + y) + 3 x(x – y) = 4 x 2 + 4 xy + 3 x 2 – 3 xy = 7 x 2 + xy 4 x 2 + 4 xy + 3 x 2– 3 xy 4 x x 4 x 3 x y x 3 x – y (5 a – b) (2 a – 3 b) = 10 a 2 – 15 ab – 2 ab + 3 b 2 = 10 a 2 – 17 ab + 3 b 2 – 15 ab – 2 ab 5 a 5 a 2 a– b– 3 b 2 a– b – 3 b

Perimeter and Area Perimeter of a shape is the total length of its sides. Perimeter of a rectangle = length + width + length + width length l width w P=l+w+l+w width w length l P = 2 l + 2 w P = 2(l + w) Area of rectangle = length width A = lw

Examples 3 x 2 x Perimeter = 3 x + 2 x + 3 x + 2 x = 10 x Area = 3 x 2 x = 6 x 2 Perimeter = 4 a + 2 b + 4 a + 2 b = 8 a + 4 b 4 a Area = 4 a 2 b = 8 ab x+5 Perimeter = x + 5 + x – 1 + x + 5 + x – 1 = 4 x + 8 x– 1 Area = (x + 5)(x – 1) = x 2 – x + 5 x – 5 = x 2 + 4 x – 5 2 b

Examples Perimeter 3 y = 4 x + 3 y + x + 2 y + 3 x + 5 y = 8 x + 10 y x 4 x 2 y A B 3 x Area of A = 4 x 3 y = 12 xy 5 y Area of B = 3 x 2 y = 6 xy Total area = 12 xy + 6 xy = 18 xy