WEBVTT

1
00:00:00.000 --> 00:00:03.077
Here is the problem: (x minus y) cubed.

2
00:00:03.527 --> 00:00:07.265
Expand (x minus y) cubed and collect like terms.

3
00:00:08.065 --> 00:00:09.261
Read the expression.

4
00:00:09.711 --> 00:00:22.029
Expand powers of sums. Write (a plus b) to the power n as repeated multiplication and multiply out; e.g. (a plus b) squared equals a squared plus 2ab plus b squared.

5
00:00:22.479 --> 00:00:24.476
Result after multiplying out.

6
00:00:24.926 --> 00:00:29.524
Write the result in standard form. Terms are ordered by descending total degree.

7
00:00:30.324 --> 00:00:37.720
So the answer is x cubed minus 3x to the power 2y plus 3xy squared minus y cubed.

8
00:00:38.170 --> 00:00:51.382
After expanding and combining like terms the expression is x cubed minus 3x to the power 2y plus 3xy squared minus y cubed, a polynomial of degree 3 with 4 terms.

9
00:00:52.182 --> 00:01:07.020
Spot check at x equals 0.73, y equals 1.14: original negative 0.068921, simplified negative 0.068921, which checks out.
