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) = 125a3 + 100a2b + 200a2b + 160ab2 + 80ab2 + 64b3 = 125a3 + 300a2b + 240ab2+ 54b3
is this correct?
I would have accepted the answer as :
volume = (5a + 4b)^3
in your expansion , the last term in the last line should be 64b^3, you had 54b^2,
probably just a typo since the previous line was ok.
(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
would this be correct now?:)
Yes, that is correct. The volume of a cube is calculated by multiplying the length of one side by itself twice, or cubing it. In this case, the side length is (5a + 4b). So, the volume of the cube can be found by cubing (5a + 4b).
To calculate this, you start by multiplying (5a + 4b) by itself three times:
(5a + 4b) * (5a + 4b) * (5a + 4b)
Expanding each multiplication step, you get:
(25a^2 + 40ab + 16b^2) * (5a + 4b)
Multiplying each term together, you get:
125a^3 + 200a^2b + 80ab^2 + 100a^2b + 160ab^2 + 64b^3
Combining like terms, you then have:
125a^3 + 300a^2b + 240ab^2 + 64b^3
So, the volume of the box is expressed as 125a^3 + 300a^2b + 240ab^2 + 64b^3.