A window in the shape of a rectangle as shown below has a width of x+5 and a length of x^2- 3x+7 express the area of the rectangle as a single polynomial in simplest form

1. distribute parentheses [tex]\left(x^2-3x+7\right)\left(x+4\right)=x^2x+x^2\cdot \:4+\left(-3x\right)x+\left(-3x\right)\cdot \:4+7x+7\cdot \:4[/tex]

2. apply +(-a)=-a rule [tex]x^2x+4x^2-3xx-3\cdot \:4x+7x+7\cdot \:4[/tex]

3. Simplify

Steps to simplify:

[tex]x^2x=x^3[/tex]

[tex]3xx=3x^2[/tex]

[tex]3\cdot \:4x=12x[/tex]

[tex]7\cdot \:4=28[/tex]

[tex]x^3+4x^2-3x^2-12x+7x+28[/tex]

4. Add like terms [tex]=x^3+4x^2-3x^2-5x+28[/tex]

5. Add like terms [tex]=x^3+x^2-5x+28[/tex]

asuwafohjames asuwafohjames · Answer 2 · 2022-05-06T12:12:24+02:00

the area of the rectangle as a single polynomial in simplest form is x³+x²-5x+28.

What is area?

Area is the space occupied by a plane object.

To calculate the area of a rectangle, we use the formula below.

Formula:

A = LW................ Equation 1

Where:

A = Area of the rectangle
L = Length of the rectangle
W = Width of the rectangle

From the question,

Given:

L = x²-3x+7
W = x+4

Substitute these values into equation 1

A = (x²-3x+7)(x+4)
A = (x²×x)+(x²×4)+(-3x×x)+(-3x×4)+(7×x)+(7×4)
A = x³+4x²-3x²-12x+7x+28
A = x³+x²-5x+28.

Hence, the area of the rectangle as a single polynomial in simplest form is x³+x²-5x+28.

Learn more about area here: https://brainly.com/question/3948796

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