Question

Expand (1-6x)^4 (1+2x)^7 in ascending powers of x up to and includeing the terms in x^3.

Answer 1

(1-6x)^4
= 1^4 + 4*1^3(-6x)^1 + 6*1^2(-6x)^2 + 4(1^1(-6x)^3 + 1(-6x)^4
= 1-24x+216x^2-864x^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)

...

1-10x-36x^2+424x^3+...