Simplifying expressions
Collecting terms Multiplying terms Dividing terms Multiply out brackets
Remember Remember BODMAS says
3 47=3×11=33
You can divide powers of
Y × X = YX •
• •
­3x the same number by
You can also do the sum like this
P × P = P2
•
subtracting the powers, so
3 47=3×43×7=33
58 2 •
–4 × 5 = –20
•
=5
Remember that a 'term' has a 6
5 So, look at the lines...
–7 × –9 = +63
•
sign, a number and a letter. The
−12 −3 3 2 x4=3×2 x3×4=6 x12
sign stays 'glued' onto the number So = The rules are
•
8 2
and letter so you can move them
2y = –6xy
×
­3x the same as for multiplying
around...
Try to follow these examples (and
remember your directed numbers)
E.G. 1. So 5x3y−3x2y is the
The steps The steps
same as 5x−3x3y2y
1. Sort out the signs
because I just moved the -3x. This 1. Sort out the signs
2. Multiply the numbers 23x −5=6x −10
1.
works out to be 2x5y
2. Cancel the numbers
3. Multiply the letters
2. −32x −1=−6x 3
3. Work out the powers of the
E.G. 2. Sometimes you have to 3. −5 3−2x =−1510x
Some examples letters
think about the directed numbers,
4. −2y 3x4 =−6xy−8y
so 7x−4y−3x−6y is the same A few examples
1. −4r×3q=−12rq
as 7x−3x−4y−6y=4x−10y
15xy
2. −6x×8y=−48xy 1. =3y Xs cancelled
A minus sign outside the bracket
5x
E.G. 3. Powers must be treated x× x×x× x=x 4
3. simply switches all the signs in
as different symbols, so in the 12x2 y 2 4
the bracket.
2. = xy
2
4. 3×r×r×h=3 r h
expression 5p2 −3p−2p2 7p , 9xy 3
If there are two brackets, just
you treat p2 as different to p, 2x×−3y×12x=−72 x 2 y
5. 21 p q3 3
giving 3. = 1. Multiply out the first
Make sure you know how the 23
14 p q 2 p
2 2 2
5p −2p 7p−3p=3p −4p
examples work, and then try the 2. Multiply out the second
Your turn, try cancelling the
ones on the practice sheet before
Try the ones on the practice sheet 3. Collect the terms!
algebraic fractions on the practice
moving on...
now before moving on... sheet... Your turn...
KPB 2009