Algebra topic so far Algebra basics Simplify expressions

Algebra topic so far • Algebra basics • Simplify expressions by collecting like terms • Directed Numbers • Simplify Expressions by multiplying

Simplifying Expressions by multiplying • What is 3 x a equal to? • It means we have three lots of a. • We simplify to 3 a • What is 5 x b equal to? • It means we have five lots of b, i. e. • b + b + b = 5 b

Simplifying Expressions by multiplying • What is a x a equal to? • Anything multiplied by itself is a square number • So a x a = a 2. • What is a x b? • a x b = ab

Simplifying Expressions by multiplying 1. Multiply the numbers first 2. Then multiply the letters 3. Put them together Example 4 n x 3 m = 12 nm

Multiplying Expressions EXAMPLES Simplify: (a) 2 xt (b) mxt = 2 t = mt (d) = 3 y x 2 m 6 my (e) t multiplied by t = t 2 (c) = 2 t x 5 10 t 3 2 (f) 2 p x 4 p = 8 p 5

Simplifying Expressions by multiplying Examples 5 a x -3 = -15 a -9 c x 5 = -45 c -4 f x -3 = 12 f -2 g x 5 g = -10 g 2 -6 h x -4 d = 24 dh

Simplifying Expressions by multiplying • -4 b 12 k -48 rw 48 m 2 -36 ab 48 ab -9 k 2 -v 2 c 2 -t 3

Title: Simplifying by Multiplying Expressions 1 2 x a = 2 a 1 1 axa= 1 3 a x 4 a = 12 a 2 1 x -2 a 1 1 1 -a x -bc = abc = -2 a 2 b 2 1 1 1 2 a b x 2 b a = 4 a 2 b 2 a 4 x a 5 = a 9 1 ab 2 a 2 2 a x 2 b = 4 ab 1 a x a = a 3 1 1 -1 a b 2 x 2 b = -2 ab 3 1 1 (ab)2 = a b x a b = a 2 b 2 (a 2 b 3)3 = a 2 b 3 x a 2 b 3 = a 6 b 9 Rules and Hints (1) Do not use a “x” sign or simply remove it 3 x a = 3 a (2) Multiply “numbers” first 3 a x 2 b = 6__ (3) Remember your negative rules -3 x 2 = -6 (4) Multiply “letters” second a x b = ab (5) If it’s the same letter add the indices (powers) (6) Remember a = a 1 so a x a = a 1 x a 1 = a 2 (7) Letters go side by side in alphabetical order 2 a x 3 b x 4 c = 24 abc (8) ab 2 means a 1 x b 1 only the b is squared (9) (ab) 2 means a 1 b 1 x a 1 b 1 = a 2 b 2 so everything inside is raised by the outside indices (power) (10) (a 3 b 2)2 when there is a bracket multiply the inside indices by what’s on the outside so here it Is a 6 b 4 Keywords: Simplify, terms, expression, indices, index, sign, co-efficient, multiply, divide

Title: Simplifying by Multiplying Expressions b 2 ab 3 d b 2 c d 3 12 t 3 c 7 abc zy 3 dc 20 xy 6 ab 40 gh 4 abc 3 ab 6 ab 24 dc -2 abc 36 st -21 abcdef Keywords: Simplify, terms, expression, indices, index, sign, co-efficient, multiply, divide

Title: Simplifying by Multiplying Expressions PLENARY 2 x _ = -10 ab -5 ab abc ( __ ) 3 = a 3 b 3 c 3 3 a x _ = 3 a 3 a 2 3 (ab 2 c 3) =a 3 b 6 c 9 2 b 3 x _ = -6 a 3 b 4 c -3 a 3 bc a 6 b 3 x a 2 b 2 = a 8 b 5 (a 2 b)3 x (ab)2 = Keywords: Simplify, terms, expression, indices, index, sign, co-efficient, multiply, divide