algebraic simplification

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

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ζ. Dr Frost. Algebraic Simplification. Objectives: Be able to simplify algebraic expressions involving addition, subtraction, multiplication and division. Starter. Instructions: Given that each square is the sum of the two expressions below it, fill in the missing expressions. 10a + 2b. - PowerPoint PPT Presentation

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Page 1: Algebraic Simplification

ζAlgebraic SimplificationDr Frost

Objectives: Be able to simplify algebraic expressions involving addition, subtraction, multiplication and division.

Page 2: Algebraic Simplification

a a + b 2a b

2a + b3a2a + b

5a + b 5a + b

10a + 2b

StarterInstructions: Given that each square is the sum of the two expressions below it, fill in the missing expressions.

?

? ? ?

? ?

Page 3: Algebraic Simplification

3b

x2

9y2

4xy3

= 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.

?

?

?

Page 4: Algebraic Simplification

x2

2x2

-3x2

3x3

-x3

y2

5xy2

4x2y

2x2y-1

+4

x

9x

5xy

ActivityGroup things which you think are considered like terms.

Page 5: Algebraic Simplification

x2 2x2 -3x2 3x3 -x3

y2

5xy2 4x2y2x2y

-1 +4x9x

5xy

ActivityAnswers:

What therefore is the rule which determines if two terms are considered ‘like terms’?

They involve the same variables, and use the same powers.

?

Page 6: Algebraic Simplification

b3 + b2 = b5

b3 + b2 = 5b

Schoolboy ErrorsTM

What is wrong with these?

Page 7: Algebraic Simplification

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?

Page 8: Algebraic Simplification

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?

Page 9: Algebraic Simplification

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?

Page 10: Algebraic Simplification

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?

Page 11: Algebraic Simplification

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)?

Page 12: Algebraic Simplification

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?

Page 13: Algebraic Simplification

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?

Page 14: Algebraic Simplification

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?

Page 15: Algebraic Simplification

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?

Page 16: Algebraic Simplification

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

÷

= x3x3

?

Page 17: Algebraic Simplification

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 ?

Page 18: Algebraic Simplification

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

8 𝑦 24 𝑦 ?

Page 19: Algebraic Simplification

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

16𝑥 𝑦24 𝑦

?

Page 20: Algebraic Simplification

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

÷

𝑥𝑧2

16𝑥2 𝑦𝑧32 𝑥𝑦

?

Page 21: Algebraic Simplification

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

÷

5 𝑥−22 x+ 9𝑥

2 𝑦3 𝑥𝑦 −2 ?

Page 22: Algebraic Simplification

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

x ( 9 𝑥 𝑦 2𝑦 )− y ( 8 𝑥2 𝑦22 𝑦2 )?