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

aa + b2ab 2a + b3a2a + b 5a + b 10a + 2b Starter Instructions: Given that each square is the sum of the two expressions below it, fill in the missing expressions. ? ??? ??

3b x2x2 9y 2 4xy 3 = 3 × b = x × x = 9 × y × y = 4 × x × y × y × y What does these actually mean? ? In terms of what we’re multiplying together. ? ? ?

x2x2 x2x2 2x 2 -3x 2 3x 3 -x 3 y2y2 y2y2 5xy 2 4x 2 y 2x 2 y +4 x x 9x 5xy Activity Group things which you think are considered like terms.

x2x2 x2x2 2x 2 -3x 2 3x 3 -x 3 y2y2 y2y2 5xy 2 4x 2 y 2x 2 y +4 x x 9x 5xy Activity Answers: What therefore is the rule which determines if two terms are considered ‘like terms’? They involve the same variables, and use the same powers. ?

b 3 + b 2 = b 5 b 3 + b 2 = 5b Schoolboy Errors TM What is wrong with these?

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 x ÷ ÷ 2x + x 2 + 5x = x 2 + 7x ?

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 x ÷ ÷ 2x + 3x 2 + 8x – 2x 2 = x x ?

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 x ÷ ÷ x 3 + x 2 + x + x = x 3 + x 2 + 2x ?

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 x ÷ ÷ x 2 y + xy 2 - x = x 2 y + xy 2 - x ?

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 x ÷ ÷ y × 3r = 3yr (or 3ry) ?

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 x ÷ ÷ 6x × 3y = 18xy ?

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 x ÷ ÷ 6x + 3y = 6x + 3y ?

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 x ÷ ÷ 12qw × q = 12q 2 w ?

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 x ÷ ÷ 3xy × 3yz = 9xy 2 z ?

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 x ÷ ÷ = x 3x 3 ?

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 x ÷ ÷ = 3x ?

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 x ÷ ÷ = 2y ?

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 x ÷ ÷ = 4xy ?

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 x ÷ ÷ ?

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 x ÷ ÷ ?

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 x ÷ ÷ ?