Question

What is the expansion of (a + b)4?

o A. a4 + a3b + a2b2 + ab3 + 64
B. a4 + 4a3b + 6a2b2 + 4ab3 + b4
C. a4 + 2a²b + 3a2b2 + 2ab3 + b4
D. a4 + 4a3b - 6a2b2 + 4ab3 – 64​

Answer 1

option B

Explanation:

`(a+b)^4\\\\=(a+b)^2(a+b)^2\\\\=(a^2+2ab+b^2)(a^2+2ab+b^2)\\\\=a^2(a^2+2ab+b^2)\\\\+2ab(a^2+2ab+b^2)\\\\+b^2(a^2+2ab+b^2)\\\\=a^4+2a^3b+a^2b^2\\\\+2a^3b+4a^2b^2+2ab^3\\\\+a^2b^2+2ab^3+b^4\\\\=a^4+4a^3b+6a^2b^2+4ab^3+b^4`