ALGEBRAIC FACTORING
Factoring is just like dismantling or separating the common part(s) of the expression from the expression itself, or from a series of expressions.
Illustration:
The common factor of two or more terms is a numerical coefficient or variable(s) that appear both in each term.
Below were the illustrations of the monomial factor.
1.
(ax + ay) = a (x + y)
2.
(3ab – 6ax) = (3ab-2.3ab) = 3a (b -2x )
3.
(2x2y - 4xy+6y2) = (2.x.x.y - 2.2.x.y + 2.3.y.y) = 2y(x2
-2x + y)
FACTORING THE DIFFERENCE OF TWO SQUARES:
a2 – b2 = (a - b)(a + b) or (a +
b)(a - b)
example:
x2-4=x2-22=(x+2(x-2)

FACTORING THE TRINOMIAL PERFECT SQUARE:
1. (a + b)2
= a2 + 2ab + b2
example:
(a+3)2 = a2 + 2(3a) +32
= a2 +
6a + 9
2. (a - b)2
= a2 - 2ab + b2
example:
(x-3)2 = x2 -2(3x)+ 32
= x2
- 6x + 9
FACTORING THE TRINOMIAL OF OTHER FORMS:
1. a2 + a (x+ y) + x y = ( a + x )(a + y)
example:
b2+5b+6 = b2+ b(3+2)+2(3)=(b+2)(b+3)
2. acx2 + (ad + b c )x + b d = ( ax + b )( cx + d )
example:
6x2 + 19x + 15 = 2x(3x) + 2x(5)+ 3(3x) + 3(5)
= 6x2
+ 10x + 9x + 15
=(2x+3)(3x+5)
FACTORING THE SUM and DIFFERENCE OF TWO CUBES:
1.
a3 + b3 = ( a + b )( a3
–a b + b3 )
example:
x3 + 23 = (x + 2)(x3 -
2x + 23)
= (x +
2)(x3 - 2x + 8)
2.
a3 – b3 = ( a – b )( a3
+ a b + b3 )
example:
x3 - 33 = (x - 3)(x3 +
3x + 33 )
= (x - 3)(x3
- 3x + 27)
EXERCISES:
Factor the following:
1.(2x – 2y) =
2.(2x + 4y) =
3.(3x – 6y + 9z) =
4.( 2a + 3b – c)2 =
5. -2( 4a – 8b) =
6.(2x2
y - 4xy+6y2) =
7.(4ax2 y – 2axy+12ay2) =
8.(a2 – 4) =
9.(a2 – 4)2 =
10.(9x2 – 4y2) =
11.(a+2bc) 2 =
12.(a +b - c)2 =
13.( m3 + n2 )2 =
14.( x3 – 8 ) =
15.( 27m3 + 8n3) =