The edge of the cube was equal to a m. It was increased x times, and then lengthened by z m.

The edge of the cube was equal to a m. It was increased x times, and then lengthened by z m. By how many m3 and how many times did the volume of the cube increase?

We can find the volume of a cube by raising the length of its edge to the third power, or:

V = a ^ 3.

Now we multiply the edge x times, that is, ax, and then lengthen it by z m, or ax + z, and find the volume of a cube with this edge size:

V ‘= (ax + z) ^ 3 = (ax) ^ 3 + 3 (ax) ^ 2z + 3axz ^ 2 + z ^ 3

Let’s find how much the volume will increase. Subtract the previous volume value:

V – V ‘= (ax) ^ 3 + 3 (ax) ^ 2z + 3axz ^ 2 + z ^ 3 – a ^ 3 meters

Now let’s find how many times the volume of the cube has increased:

V / V ‘= ((ax) ^ 3 + 3 (ax) ^ 2z + 3axz ^ 2 + z3) / a ^ 3 times

Answer: on (ax) ^ 3 + 3 (ax) ^ 2z + 3axz ^ 2 + z ^ 3 – a ^ 3 meters, in ((ax) ^ 3 + 3 (ax) ^ 2z + 3axz ^ 2 + z ^ 3) / a ^ 3 times.