Question

blankets with vivid patterns. the quadratic expression ((x + 2)^2 - 4) is one way to represent the area of a rectangular diné blanket, where (x) represents the width of the blanket, in feet. a partially complete equivalent form of the quadratic expression is shown below. determine the equivalent form of the expression. then, use the drop-down menus to explain the meaning of the equivalent form. equivalent form: (x (square)) click the arrows to choose an answer from each menu. the completed equivalent form of the quadratic expression is choose... . this equivalent form represents choose... of the blanket. the width of the blanket is

Explanation:

Step1: Expand the original expression

We start with the original quadratic expression \((x + 2)^2-4\). First, expand \((x + 2)^2\) using the formula \((a + b)^2=a^2+2ab + b^2\), where \(a=x\) and \(b = 2\). So \((x + 2)^2=x^2+4x + 4\). Then subtract 4: \(x^2+4x+4 - 4=x^2+4x\).

Step2: Factor the expanded expression

Now, factor the expression \(x^2+4x\). We can factor out an \(x\) from each term. So \(x^2+4x=x(x + 4)\).

Answer:

The completed equivalent form of the quadratic expression is \(x(x + 4)\). This equivalent form represents the product of the width (\(x\)) and the length (\(x + 4\)) of the blanket (since the area of a rectangle is length times width, and we factored the area expression into \(x\) times \((x + 4)\)).