Question

expand (1-x^2)^6

Answer 1

-The signs of an (a-b)^n will alternate positive, then negative, etc.
-recall pascal's triangle; this will help you with the coefficients

this website will help guide you through the problem:
algebralab[dot]org[forward slash]lessons[forward slash]lesson[dot]aspx?file=Algebra_BinomialExpansion.xml

Answer 2

(1 -X^2)^6 =
(1 - X^2)^2(1 - X^2)^2(1 - X^2)^2(1 -X^2),
(X^4 - 2X^2 + 1)(X^4 - 2X^2 +1)(X^4 - 2X + 1),
(X^8 - 2X^6 + X^4 - 2X^6 + 4X^4 -2X^2 + X^4 - 2X^2 +1)(X^4 - 2X^2 + 1)
Combine like-terms:
(X^4 - 2X^2 + 1)(X^8 - 4X^6 + 6X^4 -4X^2 + 1),
Multiply to remove parenthesis:
X^12 - 4X^10 + 6X^8 - 4X^6 + X^4
- 2X^10 + 8X^8 - 12X^6 + 8X^4 - 2X^2
+ X^8 - 4X^6 + 6X^4 - 4X^2 + 1

Combine like-terms:

X^12 - 6X^10 +15X^8 - 20X^6 + 15X^4
- 6X^2 + 1.

Since our given binomial was raised to the 6th power, our final results should be 7 terms. Always 1 greater
than the exponential.