Expanding and Simplifying Algebraic Expressions Lesson Aims: To be able to simplify algebraic expressions To be able to expand a single bracket, including negative numbers

Review of Algebraic Expressions So far we have learned that: 2c means 2 multiplied by c z means z divided by six. 6

What is the value of this expression? y when y = 4

What is the value of this expression? y when y = 4 (4 x 4) + 5 = = 21

Is this true for any number? a + b = b + a (hint: does = 3 + 4? Imagine that a and b are numbers. Does it matter what order we use to add them?

Is this true for any number? a - b = b - a (hint: does = 5 - 7? Imagine that a and b are numbers. Does it matter what order we use to subtract them?

Simplifying Expressions 2p + 4p = +

Simplifying Expressions 2p + 4p = So 2p + 4p = 6p + =

Simplifying Expressions 2a + 3a = +

Simplifying Expressions 2a + 3a = + = 2a +3a = 5a

Simplifying Expressions 2a + p = +

Simplifying Expressions We can only simplify when the terms have the same letter or variable. 2a + p = + = 2a + p

Simplifying Expressions 2a + p + 4a + 2k + 3p =

Simplifying Expressions 2a + p + 4a + 2k + 3p = First look at a: Then look at p: Then look at k:

Simplifying Expressions 2a + p + 4a + 2k + 3p = First look at a: 2a + 4a = 6a Then look at p: Then look at k:

Simplifying Expressions 2a + p + 4a + 2k + 3p = First look at a: 2a + 4a = 6a Then look at p: p + 3p = 4p Then look at k:

Simplifying Expressions 2a + p + 4a + 2k + 3p = First look at a: 2a + 4a = 6a Then look at p: p + 3p = 4p Then look at k: 2k

Simplifying Expressions 2a + p + 4a + 2k + 3p = First look at a: 2a + 4a = 6a Then look at p: p + 3p = 4p Then look at k: 2k So the expression becomes: 6a + 4p + 2k

Expanding Brackets 3(a + 5) What does this mean? ‘add five to a then multiply the whole lot by three’ Or ‘three lots of a added to three lots of 5

Expanding Brackets 3(a + 5) + 5 a a a

Expanding Brackets 3(a + 5) + 5 a a a 3(a + 5) =

Expanding Brackets 3(a + 5) + 5 a a a 3(a + 5) = (3 x a) +

Expanding Brackets 3(a + 5) + 5 a a a 3(a + 5) = (3 x a) + (3 x 5) =

Expanding Brackets 3(a + 5) + 5 a a a 3(a + 5) = (3 x a) + (3 x 5) = 3a + 15

Expanding Brackets 6(2a + 4) + 4 6(2a + 4) = + 4 (6 x 2a) + (6 x 4) = 12a + 24

Expanding Brackets Example: 5(2z – 3) Each term inside the brackets is multiplied by the number outside the brackets. Watch out for the signs!

Expanding Brackets Example: 5(2z – 3) (5 x 2z) – 5 x 3

Expanding Brackets Example: 5(2z – 3) (5 x 2z) – 5 x 3 = 10z – 15

Expanding Brackets Example: 2(3p + 4) + 3(4p + 1)

Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4)

Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1)

Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1) = 6p + 8

Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1) = 6p p + 3

Expanding Brackets Example: 2(3p + 4) + 3(4p + 1) = (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1) = 6p p + 3 = 18p + 11

Solving with brackets 3(2x+1) 2x + 1 How many x’s do I have in total? ______ What is the total value of my numbers? ___ 6x +3 3(2x+1) =6x + 3

Solving with brackets 2(3a+2) 3a (3a+2) =6a +4

3 (3b+4) =9b + 12 Remember: 1.Write out the question. 2.Multiply what is outside the bracket by the first thing inside the bracket. 3.Multiply what is outside the bracket by the last thing inside the bracket.