This pattern of addition continues down the triangle!
1 1+1 1+2+1 1 3 3 1
0th Row 1st Row 2nd Row 3rd Row
Fairy: Now let's take a closer look at the first few rows. Notice how the number one outlines the triangle.
Why You're Wrong
Fairy: Now look at the 1st row. 1+1=2, which is the middle number in the 2nd row and the ones on the side come down. Add 1 and 2 from the second row to make 3 on both sides. Then bring down the ones.
Here's An Example
Because the exponent is to the 3rd power, we use the coefficients from the 3rd row in Pascal's Triangle.
1 1 1 1 2 1 1 3 3 1
Byron: That kind of makes sense! Wait why is the very first row the 0th row and not the 1st row?
A Happy Ending
See, Byron! Pascal's Triangle isn't so hard!
Fairy: You see, if you're taking a binomial to the 0th power or the 1st power, those numbers in the triangle are the coefficient of the bionomial. Let's try an example!
Instead of FOIL-ing or expanding, we can use Pascal's Triangle!
Fairy: Then we insert the variables "a" and "b". The exponents for "a" start at the 3rd power and decrease to zero through the rest of the equation. The exponents for "b" start at zero and increase to the 3rd power through the rest of the equations.
Thanks Algebra II Fairy! Thanks to you I can ace my test now!