FACTORIZATION OF ALGEBRAIC EXPRESSIONS

CONTENT

1. Expansions Leading to Quadratic Expressions
2. Factorization of Quadratic Expressions
3. Difference of Two Squares
4. Algebraic Fractions With Monomial Denominators

Expansions Leading to Quadratic Expressions

A quadratic expression is one in which \(2\) is the highest power of the unknown(s) in the expression. For example,

\(x^2 -4x -12\),  \(16 -a^2\),  \(3x^2 + 17xy + 10y^2\) are all quadratic expressions.

Example:

Expand:

(a) \((a + 3) (a -4)\)

(b) \((2x + 3) (4x -5)\)

Solution:

(a) \((a + 3) (a -4)\) \(= a (a -4) + 3(a -4)\)

\(= a^2 -4a + 3a -12\)

\(= a^2 -a -12\)

(b) \((2x + 3) (4x -5)\) \(= 4x (2x + 3) -5(2x + 3)\)

\(= 8x^2 + 12x -10x -15\)

\(= 8x^2 + 2x -15\)

(c) \((4m -n)(3m -n) \) \(= 4m(3m -n) -n(3m -n)\)

\(= 12m^2 -4mn -3mn + n^2\)

\(= 12m^2 -7mn + n^2\)

Alternative Method

1.