WEBVTT

1
00:00:00.000 --> 00:00:03.936
Here is the problem: (2x minus 1) to the power 4.

2
00:00:04.386 --> 00:00:07.985
Expand and simplify the polynomial into standard form.

3
00:00:08.785 --> 00:00:18.061
Distribute every product and power. Multiply each term of one factor by each term of the other; expand powers by repeated multiplication.

4
00:00:18.511 --> 00:00:21.019
Combine like terms and order by degree.

5
00:00:21.469 --> 00:00:27.193
Read off the key features. degree 4, leading coefficient 16, constant term 1.

6
00:00:27.993 --> 00:00:36.561
So the answer is 16x to the power 4 minus 32x cubed plus 24x squared minus 8x plus 1.

7
00:00:37.011 --> 00:00:51.117
In standard form the polynomial is 16x to the power 4 minus 32x cubed plus 24x squared minus 8x plus 1 (degree 4, leading coefficient 16, constant term 1).

8
00:00:51.917 --> 00:00:57.710
Spot check at x equals 2: original and expanded form both give 81.