% why is it BAD to open brackets if you compute (1-x)^7 for an x near 1:
x = 0.988:.0001:1.012;
y = x .^7-7*x.^6 + 21*x.^5 - 35*x.^4+35*x.^3-21*x.^2+7*x-1;
y1=(x-1).^7;
plot(x,y,'b',x,y1,'r','LineWidth',2)
axis tight;grid on;xlabel('x');ylabel('y');
title('red - (x-1)^7, blue - as a sum of powers of x');