Part B: The area of a rectangle is (4x2 − 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points)



Answer :

Answer:

(2x + 3y) (2x - 3y)

Step-by-step explanation:

Recall the difference of square formula: [tex]a^2-b^2=(a+b)(a-b)[/tex].

(a + b) and (a - b) are our dimensions, or side lengths!

In this case,

[tex]a^2=4x^2[/tex]

[tex]b^2= 9y^2[/tex]

Using that formula, just square root a and b to find the dimensions!

[tex]\sqrt{a^2} =\sqrt{4x^2} =2x[/tex]     ([tex]x^2[/tex] is just x*x, like how 4 is 2*2)

[tex]\sqrt{b^2}=\sqrt{9y^2} =3y[/tex]

So,

(a + b) = (2x + 3y)

(a - b) = (2x - 3y)