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 3a What is 5 x b equal to? It means we have five lots of b, i.e. b + b + b + b + b = 5b

Simplifying Expressions by multiplying What is a x a equal to? Anything multiplied by itself is a square number So a x a = a2. What is a x b? a x b = ab

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

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

Simplifying Expressions by multiplying Examples 5a x -3 = -9c x 5 = -4f x -3 = -2g x 5g = -6h x -4d = -15a -45c 12f -10g2 24dh

Simplifying Expressions by multiplying -4 × -3k = -8r × 6w = -8m × -6m = 4a × -9b = -6ab × -8 = -9k × k = -v × v = -c × –c = -t2 × t = -4b 12k -48rw 48m2 -36ab 48ab -9k2 -v2 c2 -t3

Title: Simplifying by Multiplying Expressions 2 x a = 2a Rules and Hints Do not use a “x” sign or simply remove it 3 x a = 3a Multiply “numbers” first 3a x 2b = 6__ Remember your negative rules -3 x 2 = -6 Multiply “letters” second a x b = ab If it’s the same letter add the indices (powers) Remember a = a1 so a x a = a1 x a1 = a2 Letters go side by side in alphabetical order 2a x 3b x 4c = 24abc (8) ab2 means a1 x b1 x b1 only the b is squared (9) (ab) 2 means a1b1 x a1b1 = a 2 b 2 so everything inside is raised by the outside indices (power) (10) (a3b2)2 when there is a bracket multiply the inside indices by what’s on the outside so here it Is a6b4 a x a = 1 1 a2 2a x 2b = 4 ab a x a x a = 1 1 1 a3 3a x 4a = 1 1 12 a2 2a b x 2b a = 1 1 1 1 4 a2b2 a4 x a5 = a9 -a x -bc = abc 1 1 - a b2 x 2b = -2 ab2 x -2a = -2 a2b2 1 1 1 ab3 (ab)2 = a b x a b 1 1 1 1 = a2b2 (a2b3)3 = = a6b9 a2b3 x a2b3 x a2b3 Keywords: Simplify, terms, expression, indices, index, sign, co-efficient, multiply, divide

Title: Simplifying by Multiplying Expressions b2c d3 b2 ab zy 3d 3dc 12t3c 7abc 6ab 20xy 40gh 4abc 3ab 6ab -2abc 36st -21abcdef 24dc Keywords: Simplify, terms, expression, indices, index, sign, co-efficient, multiply, divide

Title: Simplifying by Multiplying Expressions PLENARY 2 x _ = -10ab 3a x _ = 3a3 2b3 x _ = -6a3b4c -5ab a2 -3a3bc abc 3 a6 b3 x a2b2 = a8 b5 ( __ ) 3 = a3b3c3 (ab2c3) =a3b6c9 (a2b)3 x (ab)2 = Keywords: Simplify, terms, expression, indices, index, sign, co-efficient, multiply, divide