FSMQ Algebraic expressions

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Photo-copiable A Resource for Free-standing Mathematics Units Algebraic Expressions Algebraic Terms 2 a means 2 × a ab means a × b a 2 means a × a a 3 means a × a × a b a means a ÷ b c b a 2 means a × a × b ÷ c Adding and subtracting terms You can only add or subtract terms if they are the same type of terms. It may help to think of a thermometer when combining positive and negative terms. Examples 5 x – 4 y + 2 x + 6 y = 7 x + 2 y a 2 + 3 ab – 4 b 2 + 2 a 2 – 5 ab – 7 b 2 = 3 a 2 – 2 ab – 11 b 2 Expanding a bracket When there is a number (or letter) in front of a bracket, it means everything inside the bracket must be multiplied by that number (or letter). Remember the rules for signs when multiplying or dividing positive and negative quantities: Examples 1 2 3 x = 3 6 x b a a = ab a 2 Expanding 2 brackets When two brackets are multiplied, each term in the first is multiplied by each term in the second. Examples 3 2 x 5 4 x = 15 12 10 8 x x x 2 = 15 2 8 x x 2 Here are more examples of expanding brackets and simplifying. Examples 5( x – 2 y ) 2(2 x – 3 y ) = 5 x – 10 y – 4 x + 6 y = x – 4 y 4 x ( x + y ) + 3 x ( x y ) = 4 x 2 + 4 xy + 3 x 2 – 3 xy = 7 x 2 + xy (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 The Nuffield Foundation 1 x 2 3 1 3 Information Sheet x x 4 2 5 2 x x 4 3 5 3 a 2 + 2 a 2 3 ab – 5 ab – 4 b 2 – 7 b 2 a a b a When signs are the same + + or

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