1. Collecting Like Terms Lesson 31

2. Terms Literal Coefficients – are variables (letters) that represent unknown numbers. Numerical coefficients – are numbers Terms – are made up of numerical and literal coefficients.

3. Like Terms Terms with identical literal coefficients are like terms. EXAMPLE: y, 3y, -2y are like terms x, -2g, 3k are not like terms Basically the variable has to be the same.

4. Like Terms Also the variable needs to be to the same power to be like terms. Example: y 2, -2y 2, 45y 2 are like terms y, -20y 2, 5y 3 are not like terms The exponent has to be the same number.

5. Try These Which are like terms? Why? 5b, 3g, -2g, 2g 2, 5g, ½g, -g

6. Solution: Which are like terms? Why? 5b, 3g, -2g, 2g 2, 5g, ½g, -g Red – like terms. ( they all have the same variable to the same power) White – not like terms.

7. Collecting Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve!

8. Combining Like Terms t + t + t+ t + t There are five variables which are like terms therefore we simply add them like we would if they were numbers. t + t + t+ t + t = 5t

9. Collecting Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! To simplify an expression we collect like terms.

10. Collecting Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! To simplify an expression we collect like terms. ‘Like terms’ include letters that are the same and numbers.

11. Collecting Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! To simplify an expression we collect like terms. ‘Like terms’ include letters that are the same and numbers. Have a look at the expression 4x + 5x -2 - 2x + 7

12. Collecting Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! To simplify an expression we collect like terms. ‘Like terms’ include letters that are the same and numbers. Have a look at the expression 4x + 5x -2 - 2x + 7

13. Collecting Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! To simplify an expression we collect like terms. ‘Like terms’ include letters that are the same and numbers. Have a look at the expression 4x + 5x -2 - 2x + 7 All the x terms can be collected together to give 7x.

14. Collecting Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! To simplify an expression we collect like terms. ‘Like terms’ include letters that are the same and numbers. Have a look at the expression 4x + 5x -2 - 2x + 7 All the x terms can be collected together to give 7x. All the numbers collected together give 5.

15. Collecting Like Terms In algebra we often get very long expressions, which we need to make simpler. Simpler expressions are easier to solve! To simplify an expression we collect like terms. ‘Like terms’ include letters that are the same and numbers. Have a look at the expression 4x + 5x -2 - 2x + 7 All the x terms can be collected together to give 7x. All the numbers collected together give 5. So 4x + 5x -2 - 2x + 7 simplified is 7x + 5.

16. Collecting Like Terms Eg:- Simplify this expression: x + 5 + 3x - 7 + 9x + 3 - 4x

17. Collecting Like Terms Eg:- Simplify this expression: x + 5 + 3x - 7 + 9x + 3 - 4x Here's how to do it in easy steps:

18. Collecting Like Terms Eg:- Simplify this expression: x + 5 + 3x - 7 + 9x + 3 - 4x Here's how to do it in easy steps: Write down the expression. x + 5 + 3x - 7 + 9x + 3 - 4x

19. Collecting Like Terms Eg:- Simplify this expression: x + 5 + 3x - 7 + 9x + 3 - 4x Here's how to do it in easy steps: Write down the expression. x + 5 + 3x - 7 + 9x + 3 - 4x Collect all the terms together which are alike. Remember that each term comes with an operation (+,-) which goes before it. x + 3x + 9x - 4x + 5 - 7 + 3

20. Collecting Like Terms Eg:- Simplify this expression: x + 5 + 3x - 7 + 9x + 3 - 4x Here's how to do it in easy steps: Write down the expression. x + 5 + 3x - 7 + 9x + 3 - 4x Collect all the terms together which are alike. Remember that each term comes with an operation (+,-) which goes before it. x + 3x + 9x - 4x + 5 - 7 + 3 Simplify the x terms. x + 3x + 9x - 4x = 9x

21. Collecting Like Terms Eg:- Simplify this expression: x + 5 + 3x - 7 + 9x + 3 - 4x Here's how to do it in easy steps: Write down the expression. x + 5 + 3x - 7 + 9x + 3 - 4x Collect all the terms together which are alike. Remember that each term comes with an operation (+,-) which goes before it. x + 3x + 9x - 4x + 5 - 7 + 3 Simplify the x terms. x + 3x + 9x - 4x = 9x Simplify the numbers separately. 5 - 7 + 3 = 1

22. Collecting Like Terms Eg:- Simplify this expression: x + 5 + 3x - 7 + 9x + 3 - 4x Here's how to do it in easy steps: Write down the expression. x + 5 + 3x - 7 + 9x + 3 - 4x Collect all the terms together which are alike. Remember that each term comes with an operation (+,-) which goes before it. x + 3x + 9x - 4x + 5 - 7 + 3 Simplify the x terms. x + 3x + 9x - 4x = 9x Simplify the numbers separately. 5 - 7 + 3 = 1 The simplified expression is: 9x + 1

23. Collecting Like Terms Eg:- Simplify this expression: 5x + 3y - 6x + 4y + 3z

24. Collecting Like Terms Eg:- Simplify this expression: 5x + 3y - 6x + 4y + 3z Collect the like terms together - ie, re-order them 5x - 6x + 3y + 4y + 3z

25. Collecting Like Terms Eg:- Simplify this expression: 5x + 3y - 6x + 4y + 3z Collect the like terms together - ie, re-order them 5x - 6x + 3y + 4y + 3z Simplify your expression, x first 5x - 6x = -x

26. Collecting Like Terms Eg:- Simplify this expression: 5x + 3y - 6x + 4y + 3z Collect the like terms together - ie, re-order them 5x - 6x + 3y + 4y + 3z Simplify your expression, x first 5x - 6x = -x then simplify y 3y + 4y = 7y

27. Collecting Like Terms Eg:- Simplify this expression: 5x + 3y - 6x + 4y + 3z Collect the like terms together - ie, re-order them 5x - 6x + 3y + 4y + 3z Simplify your expression, x first 5x - 6x = -x then simplify y 3y + 4y = 7y then simplify z 3z

28. Collecting Like Terms Eg:- Simplify this expression: 5x + 3y - 6x + 4y + 3z Collect the like terms together - ie, re-order them 5x - 6x + 3y + 4y + 3z Simplify your expression, x first 5x - 6x = -x then simplify y 3y + 4y = 7y then simplify z 3z The answer is: -x + 7y + 3z.

29. Collecting Like Terms We can extend this idea to terms involving powers, but we must remember the following rule: x is not the same as x 2

30. Collecting Like Terms We can extend this idea to terms involving powers, but we must remember the following rule: Eg:- Simplify the following expression 3x + 5 + x 2 - 2x + 2x 2 - 1 x is not the same as x 2

31. Collecting Like Terms We can extend this idea to terms involving powers, but we must remember the following rule: Eg:- Simplify the following expression 3x + 5 + x 2 - 2x + 2x 2 - 1 Rearrange the expression so that like terms are next to each other: x 2 + 2x 2 + 3x - 2x + 5 - 1 x is not the same as x 2

32. Collecting Like Terms We can extend this idea to terms involving powers, but we must remember the following rule: Eg:- Simplify the following expression 3x + 5 + x 2 - 2x + 2x 2 - 1 Rearrange the expression so that like terms are next to each other: x 2 + 2x 2 + 3x - 2x + 5 - 1 And then simplify: NB: Expressions of this type are usually written with the 'x 2 ' term first, then the 'x' term and finally the number term. x is not the same as x 2 3x 2 + x + 4

33. Collecting Like Terms Try these questions in your classwork books now: Simplify the following: 1)4y + x – 2y – x + 3x 2)x + 2x + 3y + 4z - y 3)-y + 3z – 2y + 4 4)x + y 2 + 2y – 7 – 2x + y 5)3xy + x 2 + y – 2yx