00:01
Okay, we've been given the expression ax plus by for power of 5 and we'd like to expand this binomially.
00:06
So our first term we'll have by for power of 0, anything's power of 0 is 1, so we'll have to worry about that.
00:12
And we'll have 5 choose 0 which is also 1, so anything we have to worry about is a x to the power of 5.
00:18
So our first term is 8 to power of 5, x to the power of 5.
00:23
Our next term, it'll be 5 choose 1, so we're just going to have 5.
00:28
We're taking one off of our ax powers, so we'll just have a to power of 4, x power of 4, and we'll be taking one of one power of our by.
00:42
Our next expression, we'll have 5 choose 2, which 5 choose 2 should be 10, but i'm going to check that on my calculator.
00:55
That is indeed, so we will have 10.
00:57
We're taking one of off our a powers, so we'll have aq.
01:00
Cubed, x cubed, and we're adding one to our second term, so we'll have b squared, y square.
01:08
Remembering pascal's triangle, our next term, five choose three, this is five to zero, five choose two, five choose three is also going to be ten...