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Contents
Simple
Algebraic Expressions
Evaluation of Algebraic Expression
Rules
of Algebra
Algebraic
Fractions
Quiz
1
Expansion:
The Foil Method
Algebraic
Identities
Basic
Factorisation
Factorisation
of Quadratic Polynomials
Factorisation by
Grouping
Quiz
2
Long
Division
Polynomial
Identities
Quiz
3
Algebra
Main Page
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Factorisation
by Grouping Expressions
can be factorised by the method of grouping.
Sometimes, it is possible to find a common factor by grouping terms.
 x2
- xy + bx - by
= x(x - y)+b(x - y)
= (x - y) (x + b)
At other times, it may be necessary to re-group the terms of an expression in
order to find the common factor.
Example 2:
xd + yc +xc +yd
= (xd + xc) (yc +yd)
= x(d +c) y(c + d)
= (d + c ) (x + y)
Factorisation may be simplified by changing the signs of the
factors
4(a - b)+ x(b - a)
= (a - b) (4 -x)
Example
4:
x3 - x2 - 1 + x
= x2(x - 1) - (1 - x)
= x2(x - 1) +(x
- 1)
= (x2 +1) (x - 1)
Example 5:
r2 - s2 -4 r -4 s
= (r + s) (r - s) -4(r +
s)
= (r + s) (r - s - 4)
Example 6:
t3 - 125 + 5t2 -25t
= t3
+ 5t2 -25t- 125
= t2 (t +
5) -25(t + 5)
= (t2
-25) (t + 5)
= (t + 5) (t - 5) (t + 5)
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