(x+y)to the 7th power

Question

how do i solve this using pascals triangle

Answer 1

                                                                         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

x^7  + 7x^6y + 21x^5y^2 + 35x^4y^3 + 35x^3y^4 + 21x^2y^5 + 7 xy^6 + y^7

Note that as the triangle grows downward, the numbers in the new row are the sum of the two numbers above them.

The sum of the values of the exponents always equals 7.  It absolutely beats expanding the old way.