#### notes

Division of Algebraic Expressions is the opposite process of multiplication. In algebra, the division is similar to the division done in arithmetic. In division of Algebraic-Expressions, we use the laws of exponents.

**Points to be remember: **

1) Positive number divides in positive number to get answer in positive.

2) Positive number divides in negative number to get answer in negative.

3) Negative number divides in negative number to get answer in positive.

4) Negative number divides in positive number to get answer in negative.

5) `a^m/a^n = a^(m - n)`

**Division of a monomial by another monomial :**

Consider `6x^3 ÷ 2x`

We may write 2x and `6x^3` in irreducible factor forms,

2x = 2 × x

`6x^3 = 2 × 3 × x × x × x `

Now we group factors of `6x^3` to separate 2x,

`6x^3 = 2 × x × (3 × x × x) = (2x) × (3x^2)`

Therefore, `6x^3 ÷ 2x = 3x^2`.

A shorter way to depict cancellation of common factors is as we do in division of numbers:

`77 ÷ 7 = 77 /7 = (7 xx 11)/7 = 11`

Similarly, `6x^3 ÷ 2x = (6x^3)/(2x) = (2 xx 3 xx x xx x xx x)/(2 xx x) = 3 xx x xx x = 3x^2 `