00:01
So to solve for this, we will use the pascal's triangle in order to expand the given binomial.
00:10
So since we are given a binomial that is raised to power up 7, remember that for a pascal's triangle we have here.
00:19
This is row 0, and this will be row 1.
00:24
This will be row 2.
00:26
This will be row 3.
00:28
It will be row 4.
00:29
This will be row 5 this will be row 6 this will be row 7 okay this is row 7 so since we are given a binomial that is raised the power of 7 we will use the numbers all the numbers in the 7th row so we have 1 721 35 35 21 and 7 and 1 okay so if you are not familiar with the pascal's triangle pascal's triangle gives you the coefficients of the expansion of any binomial.
01:05
And to make pascal's triangle, just remember that all the numbers on the side are one.
01:11
And then the numbers, i mean the number below two numbers is the sum of that numbers above it.
01:18
So, for example, we have here, one plus one, it's two.
01:22
Three plus three, it's six, one plus three, it's four, and so on and so forth.
01:27
So it is easy to make the pascal's triangle.
01:31
And then let us write our given which is a plus b raised to the power of 7.
01:43
So again, since we are given a binomial that is raised to the power of 7, its coefficients are therefore the numbers in the row 7 of the pascal's triangle.
01:53
So we will write here 1, 7.
01:58
Let's leave some space because we will need to write a and b later beside the numbers...