Question

A square painting has an area of 81x^2-90x+25. A second square painting has an area of 25x^2+30x+9.What is the difference of the areas of the paintings?

Answer 1

`56x^2-120x+16`

Explanation:

We have the following areas:

`\begin{gathered} 81x^2-90x+25 \\ 25x^2+30x+9 \end{gathered}`

The difference is the difference between both expressions, we calculate it as follows:

`\begin{gathered} 81x^2-90x+25-(25x^2+30x+9) \\ 81x^2-90x+25-25x^2-30x-9 \\ \text{ we group like terms:} \\ \mleft(81x^2-25x^2\mright)+\mleft(-90x-30x\mright)+\mleft(25-9\mright) \\ 56x^2-120x+16 \end{gathered}`