What is the polynomial that will represent the volume of a cube whose edge is 2x+7?
naturally, (2x+7)^3
just expand that out.
To find the polynomial that represents the volume of a cube with an edge of 2x + 7, we need to use the formula for the volume of a cube. The volume of a cube is calculated by raising the length of one of its edges to the power of 3.
In this case, the length of the edge is 2x + 7. To find the volume, we raise this expression to the power of 3:
Volume = (2x + 7)^3
Now we'll expand the expression using the binomial expansion. The binomial expansion of (a + b)^3 is given by:
(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
Here, a is 2x and b is 7:
Volume = (2x)^3 + 3(2x)^2(7) + 3(2x)(7)^2 + (7)^3
Simplifying each term, we have:
Volume = 8x^3 + 12x^2(7) + 6x(49) + 343
Further simplifying:
Volume = 8x^3 + 84x^2 + 294x + 343
Therefore, the polynomial that represents the volume of the cube with an edge of 2x + 7 is 8x^3 + 84x^2 + 294x + 343.