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The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box?


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The volume of a rectangular prism is given by the formula V lwh where l is the length of the prism w is the width and h is the height Suppose a box in the shape class=
The volume of a rectangular prism is given by the formula V lwh where l is the length of the prism w is the width and h is the height Suppose a box in the shape class=
The volume of a rectangular prism is given by the formula V lwh where l is the length of the prism w is the width and h is the height Suppose a box in the shape class=
The volume of a rectangular prism is given by the formula V lwh where l is the length of the prism w is the width and h is the height Suppose a box in the shape class=

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10a^3 + 91a^2 + 54a - 792 

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Answer:

[tex]V = (10a^3+91a^2+54a-792)[/tex]

Step-by-step explanation:

We have

[tex]V = lwh[/tex] (I), and

[tex]l=2a+11[/tex] (II)

[tex]w=5a-12[/tex] (III)

[tex]h=a+6[/tex] (IV)

We substitute the expression (II),(III) and (IV) in (I), that is

V= (2a+11)(5a-12)(a+6), solve the first one terms

[tex]V = (10a^2-24a+55a-132)(a+6)[/tex]

[tex]V = (10a^2+31a-132)(a+6)[/tex]

[tex]V = (10a^3+31a^2-132a+60a^2+186a-792)[/tex], simplifying

[tex]V = (10a^3+91a^2+54a-792)[/tex]

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