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# FACTORIZATION OF ALGEBRAIC EXPRESSIONS

CONTENT

3. Difference of Two Squares
4. Algebraic Fractions With Monomial Denominators

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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