**FACTORIZATION OF ALGEBRAIC EXPRESSIONS**

CONTENT

- Expansions Leading to Quadratic Expressions
- Factorization of Quadratic Expressions
- Difference of Two Squares
- 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.

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