Question

What are the dimensions of a rectangular box with a volume of 50b 3 + 75b2 - 2b - 3?

Answer 1

the one with ++-

Explanation:

Answer 2

`\large\boxed{(2b+3)*(5b-1)*(5b+1)}`

Explanation:

The formula of a volume of a rectangular box:

`V=lwh`

l - lenght

w - width

h - height

`V=50b^3+75b^2-2b-3=25b^2(2b+3)-1(2b+3)\\\\=(2b+3)(25b^2-1)=(2b+3)(5^2b^2-1^2)\\\\=(2b+3)\bigg((5b)^2-1^2\bigg)\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(2b+3)(5b-1)(5b+1)`

Therefore the dinemsions of thisp prism are:

`(2b+3)*(5b-1)*(5b+1)`