Question

multiply monomials by polynomials (basic): area model
a rectangle has a height of x and a width of 7x - 4.
express the area of the entire rectangle.
expression should be expanded.

Explanation:

Step1: Recall area formula

The area formula for a rectangle is $A = \text{height}\times\text{width}$. Here, height $h=x$ and width $w = 7x - 4$. So $A=x(7x - 4)$.

Step2: Apply distributive property

Using the distributive property $a(b - c)=ab - ac$, where $a = x$, $b = 7x$ and $c = 4$. We get $A=x\times7x-x\times4$.

Step3: Simplify terms

$x\times7x=7x^{2}$ and $x\times4 = 4x$. So $A = 7x^{2}-4x$.

Answer:

$7x^{2}-4x$