Question

Jean is framing a painting that is a rectangle. What is the perimeter of the frame?

Short answer

The perimeter of the frame is $\mathbf{4}{\mathit{x}}^{\mathbf{2}}\mathbf{+}\mathbf{4}\mathit{x}\mathbf{+}\mathbf{8}$.

Step-by-step solution

Step 1. Define standard form of a polynomial.

The standard form of a polynomial means, writing the polynomial in descending powers of the variable.

Step 2. Define like and unlike terms.

In algebra, like terms are the terms that have the same variables and powers.

The unlike terms are two or more terms that are not like terms.

Step 3. Define the perimeter of a rectangle.

Perimeter of a rectangle is defined as

$P=2\left(L+W\right)$

Where,

$P\mathit{=}$Perimeter of the rectangle

$L=$Length of the rectangle

$W=$Width of the rectangle

Step 4. Calculate the perimeter for the given rectangle.

Observe the given rectangle.

$L=2x^2-3x+1$

$W=5x+3$

Substitute the value of$L$ and$W$ in$P=2\left(L+W\right)$

$\begin{array}{c}P=2\left(\left(2x^2-3x+1\right)+\left(5x+3\right)\right)\\ =2\left(2x^2-3x+1+5x+3\right)\end{array}$

Combine the like terms

$\begin{array}{c}P=2\left(2x^2-3x+5x+3+1\right)\\ =2\left(2x^2+2x+4\right)\\ =2\left(2x^2\right)+2\left(2x\right)+2\left(4\right)\\ =4x^2+4x+8\end{array}$

Therefore the perimeter of the frame is $4x^2+4x+8$.