Question

The Johnsons’ new swimming pool measures 3x^2-2x+1 ft in length and x+2 ft in width. What is the area of the new swimming pool, in square feet?

Answer 1

Answer:

$3x^3 + 4x^2 -3x + 2$

Step-by-step explanation:

The area of the swimming pool will be equal to $length * width$.

We know that the length is $3x^2-2x+1$ and the width is $x+2$.

Therefore we can substitute those into the equation:

$(3x^2-2x+1)(x+2)$

Then, we expand the brackets using a grid (attached).

After this, we collect like terms to find the final answer:

$3x^3+6x^2-2x^2-4x+x+2\\3x^3 + 4x^2 -3x + 2$

Our final answer is: $3x^3 + 4x^2 -3x + 2$