Algebraic Simplification

1. ζ Dr Frost Algebraic Simplification Objectives: Be able to simplify algebraic expressions involving addition, subtraction, multiplication and division.

2. Starter Instructions: Given that each square is the sum of the two expressions below it, fill in the missing expressions. 10a + 2b 5a + b 5a + b ? 2a + b 3a 2a + b ? ? a a + b 2a b ? ? ?

3. What does these actually mean? In terms of what we’re multiplying together. = 3 × b 3b ? x2 = x × x ? 9y2 = 9 × y × y ? 4xy3 = 4 × x × y × y × y ?

4. Activity Group things which you think are considered like terms. 4x2y 9x x2 3x3 2x2 y2 x 2x2y -1 -x3 -3x2 5xy2 +4 5xy

5. Activity Answers: 9x x -1 +4 y2 5xy2 2x2y 4x2y 5xy 2x2 x2 -3x2 3x3 -x3 What therefore is the rule which determines if two terms are considered ‘like terms’? They involve the same variables, and use the same powers. ?

6. Schoolboy ErrorsTM b3 + b2 = b5 b3 + b2 = 5b What is wrong with these?

7. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ 2x + x2 + 5x = x2+ 7x ?

8. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ 2x + 3x2 + 8x – 2x2 = x2+ 10x ?

9. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ x3 + x2 + x + x = x3+ x2 + 2x ?

10. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ x2y + xy2 - x = x2y + xy2- x ?

11. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ y × 3r = 3yr (or 3ry) ?

12. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ 6x × 3y = 18xy ?

13. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ 6x + 3y = 6x + 3y ?

14. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ 12qw × q = 12q2w ?

15. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ 3xy × 3yz = 9xy2z ?

16. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ 3x 3 = x ?

17. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ = 3x ?

18. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ = 2y ?

19. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ = 4xy ?

20. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ ?

21. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ ?

22. When adding algebraic terms, we can collect like terms together. When multiplying algebraic terms, we just multiply each of the individual items. When dividing algebraic terms, we ‘cancel out’ common items. + Don’t mix up the first two! x ÷ ?