Question

The length, breadth and height of a metal box are $(x+5),(x-2)$ and $(x-1)$ respectively. What is its volume?

Answer 1

Volume of cuboid is $length\times breadth\times height$

Here, the length is $(x+5)$, breadth is $(x-2)$ and height is $(x-1)$.

Therefore, the volume of cuboid is:

$length\times breadth\times height=(x+5)(x-2)(x-1)$

Firstly multiply the first and second term as follows:

$(x+5)(x-2)(x-1)=[(x\times x)+(x\times -2)+(5\times x)+(5\times -2)](x-1)=(x^2-2x+5x-10)(x-1)$

$=(x^2+3x-10)(x-1)$

Now multiply the resulting expression:

$(x^2+3x-10)(x-1)=(x^2\times x)+(x^2\times -1)+(3x\times x)+(3x\times -1)+(-10\times x)+(-10\times -1)$

$=x^3-x^2+3x^2-3x-10x+10=x^3+2x^2-13x+10$

Hence, volume of cuboid id $x^3+2x^2-13x+10$.