Variables & Coefficients of Algebraic Expressions

In Mathematics, a variable is a quantity that can change. Letters are used to represent these changing, unknown quantities in arithmetic, 4 x 2  is a short way of writing  4  +  4.

Similarly, in algebraAlgebra is a branch of mathematics that substitutes letters for numbers. Algebra is about finding the unknown or putting real-life variables into equations and then solving them., 5 x a is a short form for  \( \scriptsize a \: + \: a \: + \: a \: + \: a \: + \: a \)

We usually shorten \(\scriptsize 5 \: \times \: a \: to \: 5a\)

\( \scriptsize 5a \\ \scriptsize= 5 \: \times \: a \\ \scriptsize = a \: + \: a \: + \: a \: + \: a \: + \: a \)

Example

Write down the coefficients of the following expressions:

i. 3a – 5b
ii. 6d² + 2d 
iii. -18ab²
iv. x² – xy³

Solution

i. The coefficient of a = 3, b = – 5

ii. The coefficient of d² = 6, d = 2

iii. The coefficient of ab² = -18

iv. The coefficient of x² = 1, xy³ = -1