Question

a rectangle has a height of 7 and a width of $2x^{2}-3$.
express the area of the entire rectangle.
expression should be expanded.
area =

Explanation:

Step1: Use the area formula for a rectangle

The area formula for a rectangle is \(A=\text{height}\times\text{width}\). Here, height \(h = 7\) and width \(w=2x^{2}-3\). So, \(A = 7\times(2x^{2}-3)\).

Step2: Apply the distributive property \(a(b - c)=ab-ac\)

Let \(a = 7\), \(b = 2x^{2}\), and \(c = 3\). Then \(7\times(2x^{2}-3)=7\times2x^{2}-7\times3\).

Step3: Simplify each term

\(7\times2x^{2}=14x^{2}\) and \(7\times3 = 21\). So the expanded form is \(14x^{2}-21\).

Answer:

\(14x^{2}-21\)