SOLUTION: I need to understand this by having it written out and simplified for me. Thank you. 3. A rectangular box is (4x + 3) feet wide, (5x - 2) feet long, and (3x + 2) feet high. Fin

Question 155240: I need to understand this by having it written out and simplified for me. Thank you.
3. A rectangular box is (4x + 3) feet wide, (5x - 2) feet long, and (3x + 2) feet high. Find the volume of this box.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A rectangular box is (4x + 3) feet wide, (5x - 2) feet long, and (3x + 2) feet high. Find the volume of this box.
.
The volume of ANY rectangular box is:
length * width * height
.
The problem gives us:
width is (4x + 3) feet
length is (5x - 2) feet
height is (3x + 2) feet
.
Therefore the volume is:
(4x + 3)(5x - 2)(3x + 2)
.
Now, we must multiply the three polynomials together. Let's start by multiplying the first two terms together. We do this by applying "FOIL". FOIL is a memory aid to remind you how to multiply them together.
Looking at our first two terms and applying FOIL:
(4x + 3)(5x - 2)
F: multiply First terms: (4x)(5x) = 20x^2
O: multiply Outer terms: (4x)(-2) = -8x
I: multiply Inner terms: (3)(5x) = 15x
L: multiply Last terms: (3)(-2) = -6
Finally, combine all results:
20x^2 -8x +15x -6
20x^2 + 7x -6
.
Recapping:
(4x + 3)(5x - 2)(3x + 2)
= (20x^2 + 7x -6)(3x + 2)
= (20x^2 + 7x -6)(3x) + (20x^2 + 7x -6)(2)
= (60x^3 + 21x^2 - 18x) + (40x^2 + 14x -12)
= 60x^3 + 21x^2 - 18x + 40x^2 + 14x -12
= 60x^3 + (21x^2 + 40x^2) + (-18x + 14x) -12
= 60x^3 + (61x^2) + (-4x) -12
= 60x^3 + 61x^2 - 4x -12 cubic feet (this is the solution)

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