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. which expression represents the volume of the following rectangular prism? h=2x+9 l= x+2 w= 3x a) 2x^2+13x+18 b) 6x^3+27x^2+54x c) 6x^3+39x^2+54x d) 18x^4+117x^3+162x^2

Solution: As given, Volume of a rectangular prism is given by the formula V = l w h, where l is the length of the prism, w is the width, and h is the height.

also , h=2x+9

l= x+2

w= 3 x

So, volume of prism= (2 x+9)(x+2)(3 x)= (3 x)(2 x+9)(x+2)→Using associative property

       =3 x[2 x(x+2)+9(x+2)]→Using (x+a)(x+b)= x(x+a)+a(x+b)=x²+(a+b)x+ab

      = 3 x [ 2 x²+ 4 x+ 9 x+18]

      = 3 x[ 2 x² +13 x+18]

 = (3 x)(2 x²) + (3 x)×(13 x) + (3 x)×(18)→ Using distributive property

= 6 x³+ 39 x² + 54 x → [ use

Option (C) is correct.

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