Question 927998

For the coefficients, use the seventh row of Pascal's triangle , or combinations formula: C(7,n-1)

keep in mind the exponents will have a sum of 7 in each term, and the first factor will decrease in power as the second increases.

{{{(x)^7*(-2y)^0+7*(x)^6*(-2y)^1+21*(x)^5*(-2y)^2+35*(x)^4*(-2y)^3 +35*(x^3)*(-2y)^4+ highlight(21(x)^2*(-2y)^5) + 7(x)^1*(-2y)^6 +(x)^0*(-2y)^7}}}

Now simplify each term:

{{{x^7 -14x^6y +84x^5y^2 -280x^4y^3 + 560x^3y^4 -highlight(672)x^2y^5 + 448xy^6 -128y^7 }}}

so, your coefficient is {{{21*(-2)^5=21*(-32)=-672}}}