Transcript Expanding_brackets[1]

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?
2
y
+5
when y = 4
What is the value of this
expression?
2
y
+5
when y = 4
(4 x 4) + 5 = 16 +5 = 21
Is this true for any
number?
a+b=b+a
(hint: does 4 + 3 = 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 7 - 5 = 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)
a
+ 5
a
a
+ 5
+ 5
Expanding Brackets
3(a + 5)
a
+ 5
a
a
3(a + 5) =
+ 5
+ 5
Expanding Brackets
3(a + 5)
a
+ 5
a
a
+ 5
3(a + 5) = (3 x a) +
+ 5
Expanding Brackets
3(a + 5)
a
+ 5
a
a
+ 5
+ 5
3(a + 5) = (3 x a) + (3 x 5) =
Expanding Brackets
3(a + 5)
a
+ 5
a
a
+ 5
+ 5
3(a + 5) = (3 x a) + (3 x 5) = 3a + 15
Expanding Brackets
6(2a + 4)
+ 4
+ 4
+ 4
+ 4
+ 4
+ 4
6(2a + 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 + 8 + 12p + 3
Expanding Brackets
Example:
2(3p + 4) + 3(4p + 1)
= (2 x 3p) + (2 x 4) + (3 x 4p) + (3 x 1)
= 6p + 8 + 12p + 3
= 18p + 11
Solving with brackets
• 3(2x+1)
2x + 1
2x + 1
2x + 1
6x
How many x’s do I have in total? ______
+3
What is the total value of my numbers? ___
3(2x+1) = 6x + 3
Solving with brackets
• 2(3a+2)
3a + 2
3a + 2
2 (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.