SIMPLIFYING ALGEBRAIC EXPRESSIONS ADDING LIKE TERMS MULTIPLYING LIKE

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

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

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

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

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

If a = 7 then a 5 = 75 =16807 So a value for the expression when a = 7 is 16807 a 5

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

Examples with numbers and letters 3 b 2 X 4 b 3 3 X 4 12 12 X b 2 X b 3 X X b. Xb. Xb b 5 Multiply the numbers together b 2 X b 3 = b 2+3 Add the powers =b 5

Simplify REMEMBER r = r 1 4 r x 6 s x r 2 x s 3 = 4 x 6 x x s 3 Multiply similar letters together by adding the powers Multiply the numbers together 24 r x r 2 x r 1+2 =24 r 3 s 4 x s 1+3 When we multiply letters and numbers first put the numbers next the letters in alphabetical order and we do not need the X sign

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

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

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

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

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