Amanufacturer 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.

125a^3 + 300a^2b + 240ab^2 + 64b^3

Step-by-step explanation:

The volume of a cube is the cube of the side length.

V = s^3

Here, the side length of the cube is 5a + 4b, so we cube 5a + 4b.

V = (5a + 4b)^3

V = (5a + 4b)(5a + 4b)(5a + 4b)

V = (25a^2 + 20ab + 20ab + 16b^2)(5a + 4b)

V = (25a^2 + 40ab + 16b^2)(5a + 4b)

V = 125a^3 + 100a^2b + 200a^2b + 160ab^2 + 80ab^2 + 64b^3

V = 125a^3 + 300a^2b + 240ab^2 + 64b^3

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.