Question

Binomial theorem Expand (5a + b)5

Answer 1

`3125a^5+3125a^4b+1250a^3b^2+250a^2b^3+25ab^4+b^5`

Explanation:

`(5a+b)^5`=

(5a+b)(5a+b)(5a+b)(5a+b)(5a+b)

woah, lets multiply 2 at a time:

(5a+b)(5a+b)=25a^2+10ab+b^2

(5a+b)(25a^2+10ab+b^2)=

125a^3+50a^2b+5ab^2+25a^2b+10ab^2+b^3

simplify:

(125a^3+75a^2b+15ab^2+b^3)(5a+b)=

(625a^4+500a^3b+150a^2b^2+20ab^3+b^4)(5a+b)=

3125a^5+3125a^4b+1250a^3b^2+250a^2b^3+25ab^4+b^5

hope this helps!