SIMPLIFYING ALGEBRAIC EXPRESSIONS ADDING LIKE TERMS MULTIPLYING LIKE TERMS SIMPLIFYING EXPRESSIONS REPLACING LETTERS WITH NUMBERS TO GET A VALUE FOR AN EXPRESSION USING FORMULAS REMOVING BRACKETS

ADDING LIKE TERMS 4 X 3 12 4a 3 + 3 + 3 + 3 Can be written in the shorter form Meaning that we have 4 bundles of 3’s 4 X 3 This gives the VALUE 12 Can be written in the shorter form a + a + a + a We cannot give a value for 4a until we are given a value for a 4a

28 If a = 7 Then by replacing a with 7 4a = 4 x(7) = 28 = 28 So a value for the expression 4a when a = 7 is 28

Some examples Simplify the following expressions Combine all the a’s together to get one term 3a + 2a = a+a+a + a+a = 5a 5b – 2b = b + b + b + b + b - b + b Take 2 b’s away from the 5 b’s = 3b

Simplifying expressions with numbers and different letters Simplify 3a + 2b + 5a + 3b + 7 WE can only add or subtract like terms to each other + 2b + 3b 7 3a + 5a + 5b 8a + 7 + 8a + 5b +7

Multiplying like terms Can be written in the shorter form 2 X 2 X 2 X 2 X2 This means that 2 is multiplied by itself 5 times 25 This gives a value 32 a X a X a X a X a Can be written in the shorter form We cannot get a value for a5 until we are given a value for a a5

If a = 7 then a5 = 75 =16807 So a value for the expression a5 when a = 7 is 16807

Some examples Simplify the following expressions 3a x a = 3 x a x a x a x a We now have 3 times a multiplied by itself 4 times = 3 a4 3b x 2b = 3 x 2 x b x b Multiply the numbers together and multiply the letters together = 6 x b2 Write product without multiplication sign = 6 b2

Examples with numbers and letters 3b2 X 4b3 3X4 X b2X b3 12 X bXb X bXbXb b2X b3 = b2+3 =b5 X 12 b5 Add the powers Multiply the numbers together

Simplify REMEMBER r = r1 4r x 6s x r2 x s3 r x r2 = 4 x 6 s x s3 x x Multiply similar letters together by adding the powers Multiply the numbers together s1+3 24 x r1+2 x When we multiply letters and numbers first put the numbers next the letters in alphabetical order and we do not need the X sign =24 r3s4

Order of operations = Not 21 5 + 2 x 3 11 In mathematics we have rules Multiplication or division is calculated before addition or subtraction Is simplified to 2 x a + 5 2a + 5 Is simplified to 6 – 2 x b 6-2b

Have you got it yet ? Simplify the following 5a 5m+ 7 5a + 9b 4j b4 8 . 3m + 2m + 7 5m+ 7 1. 2a + 3a 9. 6j – 3j + j 5a + 9b 4j 2. 3a + 4b + 2a + 5b 3. b x b x b x b b4 10. 3s x 4s x 6 72b2 4. b x b x c x c x c 11. 3 x s + 7 3s+7 b2c3 20b5 6+3d 5. 4b2 x 5b3 12. 6 + 3 x d 13 . 10n – 2 x 3n 4n 12bc 6. 3c x 4b . 5c4 14. 8b – 3 x b2 8b – 3 b2 7. 2 c 4 + 3c4

Finding values for expressions Find a value for the expression 3b when b =7 3b = 3 x (7) = 21 21 is the value of the expression Take out b and replace it with 7 Put 7 inside a bracket

Find a value for the expression 3c + b when c = 2 and b = 5 Replace c with 2 and b with 5 = 3 x (2) + ( 5) = 6 + 5 = 11 11 is the value of the expression

Find a value for the expressions a) pq b) 2p + q c) 5pq +2p d) q2 - p2 when e) 3 ( p + 2q ) f) ( p + q ) 2 when p = 3 and q = 7 a) pq b) 2p + q c) 3pq + 2p = 3 x ( 3 ) x ( 7 ) + 2 x ( 3 ) = (3) x (7) = 2 x ( 3) + ( 7 ) = 63 + 6 = 6 + 7 = 21 = 13 = 69 q2 - p2 d) e) 3 ( p + 2q ) f) ( q - p ) 2 = (7)2 - (3)2 = 3 ( (7) + 2x(3) ) = ( (7) – (3) ) 2 = 49 - 9 = 3( 7 + 6) = ( 4 ) 2 = 40 39 = 3 x 13 = = 16