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.** 6d^{2} +Â 2dÂ **iii.** -18ab^{2}**iv. **x^{2} – xy^{3}

**Solution**

**i.** The coefficient of a = 3, b = – 5

**ii.** The coefficient of d^{2} = 6, d = 2

**iii.** The coefficient of ab^{2} = -18

**iv.** The coefficient of x^{2} = 1, xy^{3} = -1

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