Post on 17-Jan-2016
ζAlgebraic SimplificationDr Frost
Objectives: Be able to simplify algebraic expressions involving addition, subtraction, multiplication and division.
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.
?
? ? ?
? ?
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.
?
?
?
x2
2x2
-3x2
3x3
-x3
y2
5xy2
4x2y
2x2y-1
+4
x
9x
5xy
ActivityGroup things which you think are considered like terms.
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.
?
b3 + b2 = b5
b3 + b2 = 5b
Schoolboy ErrorsTM
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
÷
2x + x2 + 5x= x2 + 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
÷
2x + 3x2 + 8x – 2x2
= x2 + 10x?
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?
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?
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)?
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?
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?
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?
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?
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
?
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 ?
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 2
4 𝑦?
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 𝑦2
4 𝑦?
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
?
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?
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 )?