Question

^{Use Pascal's triangle to expand the expression}

^(x + y)7

Answer 1

PASCAL'S TRIANGLE

If a row in the triangle is represented by 1 a b c ...

the rule for creating the next row is:

1 1+a a+b b+c ...

The first and last numbers on each row are 1s.

So the triangle up to the 7th row (which we need for this question) is:

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1. This is the row we need to expand (x+y)⁷:

x⁷+7x⁶y+21x⁵y²+35x⁴y³+35x³y⁴+21x²y⁵+7xy⁶+y⁷