An Algebraic expression is an expression that is built by the combination of integer constants and variables. They undergo operations such as addition, subtraction, multiplication and division. For example: \(4xy~ +~ 9\)

##### Algebraic Expression – Multiplication

Multiplication is simply repeated addition. We multiply variables and constants in an algebraic expression. For example, the area of a rectangular room is the product of length and breadth. The value of area depends on the value chosen for length and breadth. Similarly volume is the product of length, breadth and height.

## Multiplication of Monomial by Monomial

**Illustration 1:** Multiply \(5x\)

**Solution**: \(5x~\times~21y~\times~32z\)

We multiply the first two monomials and then the resulting monomial to the third monomial.

**Illustration 2:** Find the volume of a cuboid whose length is \(5ax\)

**Solution**: \(Volume\)

Therefore, \(volume\)

## Multiplying a Monomials and Polynomials

\(4a~\times~(2a^2~+~9a~+~10)\)

= \(8a^3~+~36a^2~+~40a\)

**Illustration 3:** Simplify the below algebraic expression and obtain its value for \(x\)

\(x(x~-~2)~+~5\)

**Solutio**n: \(x(x~-~2)~+~5\)

Substituting the value of \(x\)

\(3~\times~(3~-~2)~+~5\)

**Illustration 4: **Simplify the below algebraic expression and obtain its value for \(y\)

\(4y(2y~-~6)~–~3(y~-~2)~+~20\)

**Solution**: \(4y(2y~-~6)~-~3(y~-~2)~+~20\)

Substituting the value of \(y\)

\(4~\times~-1((2~\times~-1)~–~6)~–~3(-1~-~2)~+~20\)

= \(-4~(-2~-~6)~-~3(-3)~+~20\)

= \(32~+~9~+~20\)

This article covers the details of multiplication of algebraic expression. To learn more about other topics download Byju’s – The Learning App from Google Play Store and watch interactive videos. Also, take free tests to practice for exams.

‘

**Practise This Question**