Question

A student was asked to find the difference (4x - 3x + 6.7") - (2x - 6x + x'). The student's work is shown at right. Identify the student's error and give the correct difference.

Answer 1

Difference of polynomials

We want to find the following difference:

`(4x^5-3x^4+6x^2)-(7x^5-6x^4+x^3)`

We just need to remember one rule: we can add or substract the terms if and only if the exponent of x is the same.

Step 1

We distribute the parenthesis multiplication:

`-(7x^5-6x^4+x^3)=-7x^5+6x^4-x^3`

then

`\begin{gathered} (4x^5-3x^4+6x^2)-(7x^5-6x^4+x^3) \\ =4x^5-3x^4+6x^2-7x^5+6x^4-x^3 \end{gathered}`

Step 2

We combine like terms

terms with x⁵: 4x⁵ and -7x⁵

terms with x⁴: -3x⁴ and 6x⁴

terms with x³: -x³

terms with x²: 6x²

We add them:

4x⁵ - 7x⁵ = -3x⁵

-3x⁴ + 6x⁴ = 3x⁴

-x³

6x²

Then,

`\begin{gathered} (4x^5-3x^4+6x^2)-(7x^5-6x^4+x^3) \\ =-3x^5+3x^4-x^3+6x^2 \end{gathered}`