Introducing Algebra

Introducing algebra
BTEOTSSSBAT simplify equations and use substitution

In algebra:
x + 2 means two more than x
x – 3 means three less than x
x + y means add together x and y
3x means three times x. We don’t usually use a multiplication sign! So 3x = 3 x
means x divided by four.
We can also write this as x 4
x² means x multiplied by itself: x x

Write down the algebraic expression that means:
3 more than y
5 less than s
x divided by y
w multiplied by 4
f multiplied by 3 and divided by t
4 less than x multiplied by 4

Simplifying (collecting like terms)
To simplify an algebraic expression we have to collect like terms; only like terms can be added or subtracted
For example
2a + 4a = 6a
but 2a + 7b can’t be made any simpler.

Simplify these expressions
(a) a + a + a
(b) b + b + b – b
(c) 3a + 2a
(d) 3a + 2b – a

Brackets
Sometimes brackets are used in expressions e.g. 3 (x + 4)
A number next to a bracket multiplies everything inside the bracket.
So, 3 (x + 4) is the same as 3  (x + 4) =
3 x + 3  4
This can be simplified to 3x + 12.

Example
Expand 3(2x + 5)
Here the 3 multiplies the 2x as well as the 5
This gives 3 × 2x + 3 × 5 = 6x + 15.

Multiply out the brackets and if necessary simplify the expression
(a) 2 (x+3)
(b) 4 (x + 4)
(c) 5 (2x + 5)

Substitution
Substituting in a formula means replacing the letters by numbers
For example, in the formula A = lw
If l = 3 and w = 4
Then lw = 3  4 = 12

Other examples:
If a = 3 and b = 4, what is the value of a + b?
Using substitution, a + b = 3 + 4 = 7
(ii) If a = 5, what is the value of 4a?
Using substitution, 4a = 4  5 = 20
(iii) If x = 6 and y = 5, what is the value of 2xy?
Using substitution, xy = x y = 6  5 = 30
and 2xy = 2 x y = 2  6  5 = 60

When a = 7, b = 4, x = 2 and y = 5, work out the values of
a)a + b + y b) ax c) by
3a – 4 e) bx + 2 f) 3xy
3x + y h) 2b – x i) 2ax + 3y
j) ab – x k) ay + bxl) 2axy

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Introducing Algebra

by Steve Bishop on Jan 17, 2010

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