Question

An architect needs to calculate the dimensions of a rectangular, tiled kitchen in a new home.

Answer 1

`A)u^3+u^2-2`

Step-by-step explanation

Step 1

the area of a rectangle is given by

`^{}_{}Area_(rec\tan gle)=base\cdot heigth`

then

Let

`\begin{gathered} \text{base}=u^2+2u+2 \\ \text{heigth}=u-1 \end{gathered}`

now, replace

`\begin{gathered} Area_(rec\tan gle)=base\cdot heigth \\ Area_{}=(u^2+2u+2)(u-1) \\ \text{apply distributive property} \\ Area_{}=u^2\cdot u+2u\cdot u+2\cdot u-1\cdot u^2-1\cdot2u-1\cdot2 \\ Area_{}=u^3+2u^2+2u-u^2-2u-2 \\ \text{add like terms} \\ Area_{}=u^3+u^2-2 \end{gathered}`

hence, the answer is

`A)u^3+u^2-2`

I hope this helps you