A manufacturer of shipping boxes has a box shaped like a cube. The side length is
(5a + 4b). What is the volume of the box in terms of a and b? Show your work.
(5a+4b)^3 =(5a+4b)(5a+4b)(5a+4b) =(25a2+40ab+16b2)(5a+4b) = 125a^3 + 100a^2b + 200a^2b + 160ab^2 + 80ab^2 + 64b^3 = 125a^3 + 300a^2b + 240ab^2+ 64b^3
is this correct as an answer?
Alexa, I answered this for you yesterday
http://www.jiskha.com/display.cgi?id=1455679992
Your expansion is correct, but as I stated yesterday , why not just leave the answer as
Volume = (5a+4b)^3
For any given value of a and b, it would be so much easier to find the volume from the factored form, than from the expanded form.
okay..But why does it say show your work? how would I show it?
Yes, your answer is correct. The volume of the cube-shaped box can be found by raising the side length to the power of 3, which in this case is (5a + 4b)^3. To simplify the expression, you expanded (5a + 4b)^3 using the distributive property to multiply the terms within the parentheses.
You correctly performed the multiplication and obtained the simplified expression 125a^3 + 300a^2b + 240ab^2 + 64b^3. This represents the volume of the box in terms of a and b. Well done!