Factorization and Algebraic Expressions – JSS2 Mathematics Lesson Note (First Term)

Algebraic expressions

To expand algebraic expressions, those expressions will have to be in brackets. When the bracket ever moves, then any factor outside the bracket must be multiplied by each term inside the bracket.               

Example 1:  Expand d(a + c)

Solution: d * a   +   d * c = da + dc

Example 2: Expand (y + 3)( y + 4)

Solution:

= Y * Y +  Y * 4  + 3 * Y  + 3 * 4

 = Y2 + 4y + 3y + 12

Factorization of simple algebraic expression

Factorization is the reverse of expanding brackets. The first step in factorization is to take any common factor which the terms are:

Example 1: Factorise 3X2 + X

Solution:

X is common to the expression

Therefore = X(3X + 1)

Example 2: Factorize 6y3 – 4y2 – 4y

Solution:

2y is common in the expression

Therefore 2y(3y2 -2y -2

Algebraic expression with fractions

Example 1: Solve  X/3 + X- 2/5 = 6

Solution:

Find the L C M = 15

5x + 3X – 6 /15 = 6

Cross multiply

= 5X +  3X – 6 = 6*15

  8X – 6 = 90

 Add 6 to both sides = 8X – 6 + 6 = 90 + 6

8X = 96 (Divide both sides by 8)

X = 12.

Finding the lowest common factor and highest common factor in algebraic form

Example 1: Find the L C M of 4xy,8xv and 10x2y

Solution:

2  4xy        8xy     10x2y

2      2xy    4xy      5x2y

2        xy    2xy      5x2y

5        xy     xy         x2y

X        xy    x y        x2y

X          y           y         xy

Y          y      y           y

            1       1           1

L C M = 2 * 2 * 2 * 2 * 5 * X * X  * Y =  40X2Y

Example 2: find the H C F of 4xy, 8xy and 10x2y

Solution;

4xy =  2 * 2 * x * y

8xy =  2 * 2 * 2 * x * y

10x2y  = 2 * 5 * x * x * y

H C F =  2 * X  * Y =  2XY