Division of an algebraic expression by a monomial — lesson. Mathematics State Board, Class 8.

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i) Division of a monomial by another monomial:

A monomial

40 x y^{2}

is divided by another monomial

10 y

will result in

\frac{40 x y^{2}}{10 y} = \frac{10 \times 4 \times x \times y \times y}{10 \times y} = 4 xy

The result of dividing a monomial by another monomial will be a monomial.

ii) Division of a polynomial by a monomial:

Divide each term of the polynomial by the monomial to get the result of the division.

A polynomial

- 12 xy z^{3} + 60

is divided by a monomial

4 z

will result in:

\frac{- 12 xy z^{3} + 60}{4 z} = \frac{- 12 xy z^{3}}{4 z} + \frac{60}{4 z}

\begin{array}{l} = \frac{{- 12}^{- 3} \times x \times y \times z \times z \times z}{4 \times z} + {\frac{60}{4 z}}^{15} \\ = - 3 xy z^{2} + \frac{15}{z} \end{array}

Dividing any polynomial by a monomial will result in a polynomial.

The relation between the power of exponents and division of an algebraic expression by another algebraic expression:

We already learnt about the power of exponents.

\frac{a^{n}}{a^{m}} = a^{n} - a^{m}, n > m, a \neq 0.

The above law of exponents can be used to divide an algebraic expression by another, for instance:

\frac{4 x y^{2}}{2 y} = 2 x y^{2 - 1}

= 2 xy

Important!

When a monomial is divided by itself, we will get \(1\).

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2. Division of an algebraic expression by a monomial