The base of a rectangular box is x +2 cm wide and 2x+5 cm long. if the height of the box is x cm, write a polynomial in standard form which represents the box's volume
(x+2)(2x+5)(x)
2x^3 + 9x^2 + 10x
Stuff
To find the volume of a rectangular box, we multiply its length, width, and height. In this case, the width is x+2 cm, the length is 2x+5 cm, and the height is x cm.
The volume of the box can be calculated by multiplying these three dimensions:
Volume = (x + 2) * (2x + 5) * x
To simplify this expression and write it in standard form, we need to multiply the factors and combine the like terms:
Volume = (x * (2x + 5) * (x + 2))
Using the distributive property, we can expand the expression:
Volume = (2x^2 + 5x) * (x + 2)
Now, we can multiply each term of the first factor by the terms in the second factor:
Volume = 2x^3 + 4x^2 + 5x^2 + 10x
Combining the like terms gives us the final polynomial in standard form:
Volume = 2x^3 + 9x^2 + 10x