Question
13. Write the binomial expansion of (2a – 3b)4.
Answers
Henry
(2a - 3b)^4 =
(2a - 3b)^2 (2a - 3b)^2 =
(2a^2 - 12ab + 9b^2)(2a^2-12ab +9b^2)=
4a^4 - 24a^3b + 18a^2b^2 -
24a^3b + 144a^2b^2 - 108ab^3 +
18a^2b^2 - 108ab^3 + 81b^4.
Combine like-terms:
4a^4 - 48a^3b +180a^2b^2 - 216ab^3 +
81b^4.
The number of terms in the final results is always 1 greater than
thee exponent, and every other
term is positive.
(2a - 3b)^2 (2a - 3b)^2 =
(2a^2 - 12ab + 9b^2)(2a^2-12ab +9b^2)=
4a^4 - 24a^3b + 18a^2b^2 -
24a^3b + 144a^2b^2 - 108ab^3 +
18a^2b^2 - 108ab^3 + 81b^4.
Combine like-terms:
4a^4 - 48a^3b +180a^2b^2 - 216ab^3 +
81b^4.
The number of terms in the final results is always 1 greater than
thee exponent, and every other
term is positive.