Question

When you multiply the following binomials, what is the linear term (the term with x)?

(X+3) (X-5)

Answer 1

We conclude that 2x is the linear term with x.

Explanation:

Given the expression

`\left(x+3\right)\left(x-5\right)`

Multiplying the binomials

Apply FOIL method:

`\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd`

`\left(x+3\right)\left(x-5\right)=xx+x\left(-5\right)+3x+3\left(-5\right)`

Apply +(-) = - rule

`=xx-5x+3x-3\cdot \:5`

simplify

`=x^2-2x-15`

Here, 2x is the linear term with x.

It is called a linear term because the exponent of the variable is raised to the power of 1.

In other words, the degree of the linear term is 1.

Therefore, we conclude that 2x is the linear term with x.