# © Boardworks Ltd 2004 1 of 60 KS3 Mathematics A1 Algebraic expressions.

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© Boardworks Ltd 2004 1 of 60 KS3 Mathematics A1 Algebraic expressions

© Boardworks Ltd 2004 2 of 60 A1.3 Multiplying terms Contents A1 Algebraic expressions A1.1 Writing expressions A1.2 Collecting like terms A1.4 Dividing terms A1.5 Factorising expressions A1.6 Substitution

© Boardworks Ltd 2004 3 of 60 Multiplying terms together In algebra we usually leave out the multiplication sign ×. Any numbers must be written at the front and all letters should be written in alphabetical order. For example, 4 × a = 4 a 1 × b = b We dont need to write a 1 in front of the letter. b × 5 =5b5b We dont write b 5. 3 × d × c = 3 cd 6 × e × e =6e26e2 We write letters in alphabetical order.

© Boardworks Ltd 2004 4 of 60 Using index notation Simplify: x + x + x + x + x = 5 x Simplify: x × x × x × x × xx × x × x × x × x = x 5 x to the power of 5 This is called index notation. Similarly, x × xx × x = x 2 x × x × xx × x × x = x 3 x × x × x × xx × x × x × x = x 4

© Boardworks Ltd 2004 5 of 60 We can use index notation to simplify expressions. For example, 3 p × 2 p =3 × p × 2 × p =6p26p2 q 2 × q 3 = q × q × q × q × q = q5q5 3 r × r 2 =3 × r × r × r =3r33r3 2 t × 2 t =(2 t ) 2 or4t24t2 Using index notation

© Boardworks Ltd 2004 6 of 60 Look at this algebraic expression: 4( a + b ) What do do think it means? Remember, in algebra we do not write the multiplication sign, ×. This expression actually means: 4 × ( a + b ) or ( a + b ) + ( a + b ) + ( a + b ) + ( a + b ) = a + b + a + b + a + b + a + b = 4 a + 4 b Brackets

© Boardworks Ltd 2004 7 of 60 Expanding brackets then simplifying Sometimes we need to multiply out brackets and then simplify. For example, 3 x + 2(5 – x ) We need to multiply the bracket by 2 and collect together like terms. 3x3x + 10 – 2 x = 3 x – 2 x + 10 = x + 10

© Boardworks Ltd 2004 8 of 60 Expanding brackets then simplifying Simplify 4 – (5 n – 3) We need to multiply the bracket by –1 and collect together like terms. 4 – 5 n + 3 = 4 + 3 – 5 n = 7 – 5 n

© Boardworks Ltd 2004 9 of 60 Expanding brackets then simplifying Simplify 2(3 n – 4) + 3(3 n + 5) We need to multiply out both brackets and collect together like terms. 6n6n – 8 + 9 n + 15 = 6 n + 9 n – 8 + 15 = 15 n + 7

© Boardworks Ltd 2004 10 of 60 Simplify 5(3 a + 2 b ) – 2(2 a + 5 b ) We need to multiply out both brackets and collect together like terms. 15 a + 10 b – 4 a –10 b = 15 a – 4 a + 10 b – 10 b = 11 a Expanding brackets then simplifying

© Boardworks Ltd 2004 11 of 60 Algebraic multiplication square

© Boardworks Ltd 2004 12 of 60 Pelmanism: Equivalent expressions