Answer:
V(x) = 4x³ - 72x² + 308x
Step-by-step explanation:
Look at the picture.
The formula of a volume of a rectangular prism is:
V = lwh
l - length
w - width
h - height
We have
l = 22 - 2x, w = 14 - 2x, h = x
Substitute:
V = (22 - 2x)(14 - 2x)(x) use FOIL: (a + b)(c + d) = ac + d + bc + bd
V = [(22)(14) + (22)(-2x) + (-2x)(14) + (-2x)(-2x)](x)
V = (308 - 44x - 28x + 4x²)(x) combine like terms
V = (4x² - 72x + 308)(x) use the distributive property a(b + c) = ab + ac
V = (4x²)(x) + (-72x)(x) + (308)(x)
V = 4x³ - 72x² + 308x
