Posted by Shane on .
Expand (16x)^4 (1+2x)^7 in ascending powers of x up to and includeing the terms in x^3.

maths 
Steve,
(16x)^4
= 1^4 + 4*1^3(6x)^1 + 6*1^2(6x)^2 + 4(1^1(6x)^3 + 1(6x)^4
= 124x+216x^2864x^3+...
(1+2x)^7 = 1+14x+84x^2+280x^3+...
Now just work from the left
1(1+14x+84x^2+280x^3)
24x(1+14x+84x^2+280x^3)
+216x^2(1+14x+84x^2+280x^3)
864x^3(1+14x+84x^2+280x^3)
...
110x36x^2+424x^3+...