Answer:
a. [tex] 9a^3 - 9ab^2 [/tex]
b. [tex] 9a(a^2 - b^2) [/tex]
Step-by-step explanation:
a.
[tex] Volume = l*w*h [/tex]
[tex] Volume_{smaller} = l*w*h [/tex]
Where, [tex] l = 9a, w = b, h = b [/tex]
[tex] Volume_{smaller} = 9a*b*b = 9ab^2 [/tex]
[tex] Volume_{larger} = l*w*h [/tex]
Where, [tex] l = 9a, w = a, h = a [/tex]
[tex] Volume_{smaller} = 9a*a*a = 9a^3 [/tex]
Volume of the shaded figure = [tex] 9a^3 - 9ab^2 [/tex]
b. [tex] 9a^3 - 9ab^2 [/tex] expressed in factored form:
Look for the term that is common to 9a³ and 9ab², then take outside the parenthesis.
[tex] 9a^3 - 9ab^2 = 9a(a^2 - b^2) [/tex]
