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Algebraic Terms

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

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Algebraic Terms

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  1. a b pq a2b r c 6 – 3 3  4 12 = = = 4 6 6 r – p 3 = 4 q Algebraic Expressions Algebraic Terms Examples 2a means If p = 3, q = 4, r = 6 2  a 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 p3 = 3  3  3 = 27 means a a  b c = 2

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

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

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

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

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

  7. 3y 4x x 3x 2y A B 5y Examples Perimeter = 4x + 3y + x + 2y + 3x + 5y = 8x + 10y Area of A = 4x 3y = 12xy Area of B = 3x 2y = 6xy Total area = 12xy + 6xy = 18xy

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