Algebraic Expressions Algebraic Terms Examples 2a means 2  a If p = 3, q = 4, r = 6 ab means a  b 5p = 5  3 = 15 a2 means a  a qr = 4  6 = 24 a3 means a  a  a r2 = 6  6 = 36 a b means a  b p3 = 3  3  3 = 27 a2b c pq r 3  4 6 = 12 6 = means a  a  b  c = 2 r – p q 6 – 3 4 = 3 4 =

Adding and subtracting terms Examples 5x – 4y + 2x + 6y = 7x + 2y 5x + 2x – 4y + 6y 2x2 – x + 7 + x2 – 4x – 3 = 3x2 – 5x + 4 2x2 + x2 – x – 4x + 7 – 3 a2 + 3ab – 4b2 + 2a2 – 5ab – 7b2 = 3a2 – 2ab – 11b2 a2 + 2a2 + 3ab – 5ab – 4b2 – 7b2

Expanding a bracket Examples 3(2x + 1) = 6x + 3 3  2x 3  1 a(a – b) = a2 – ab a  a a  – b 4p(3p + 2q – 5) = 12p2 + 8pq – 20p 4p  3p 4p  2q 4p  – 5

Expanding 2 brackets Examples (2x – 3) (4x + 5) = 8x2 + 10x – 12x – 15 = 8x2 – 2x – 15 2x  4x 2x  5 – 3  4x – 3  5 + 10x – 12x 5(x – 2y) – 2(2x – 3y) = 5x – 10y – 4x + 6y = x – 4y 5  x 5  – 2y – 2  2 x – 2  – 3y 5x – 4x – 10y + 6y 4x(x + y) + 3x(x – y) = 4x2 + 4xy + 3x2 – 3xy = 7x2 + xy 4x  x 3x  – y 4x2 + 3x2 + 4xy – 3xy 4x  y 3x  x (5a – b) (2a – 3b) = 10a2 – 15ab – 2ab + 3b2 = 10a2 – 17ab + 3b2 5a  2a 5a  – 3b – b  – 3b – b  2a – 15ab – 2ab

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

Examples 3x 2x Perimeter = 3x + 2x + 3x + 2x = 10x Area = 3x  2x = 6x2 4a 2b Perimeter = 4a + 2b + 4a + 2b = 8a + 4b Area = 4a  2b = 8ab x + 5 x – 1 Perimeter = x + 5 + x – 1 + x + 5 + x – 1 = 4x + 8 Area = (x + 5)(x – 1) = x2 – x + 5x – 5 = x2 + 4x – 5

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