Question

Expand the given power using the Binomial Theorem. (10k – m)5

Answer 1

`(10k - m)^(5)=100000k-50000k^(4)m+10000k^(3)m^(2)-1000k^(2)m^(3)+50km^(4)-m^(5)`

Explanation:

* Lets explain how to solve the problem

- The rule of expand the binomial is:

`(a+b)^(n)=(a)^(n)+nC1(a)^(n-1)(b)+nC2(a)^(n-2)(b)^(2)+nC3(a)^(n-3)(b)^(3)+...............+(b)^(5)`

∵ The binomial is
`(10k-m)^(5)`

∴ a = 10k , b = -m and n = 5

∴
`(10k-m)^(5)=(10k)^(5)+5C1(10k)^(4)(-m)+5C2(10k)^(3)(-m)^(2)+5C3(10k)^(2)(-m)^(3)+5C4(10k)^(1) (-m)^(4)+5C5(10k)^(0)(-m)^(5)`

∵ 5C1 = 5

∵ 5C2 = 10

∵ 5C3 = 10

∵ 5C4 = 5

∵ 5C5 = 1

∴
`(10k-m)^(5)=100000k^(5)+(5)(10000)k^(4)(-m)+(10)(1000)k^(3)(m^(2))+(10)(100)k^(2)(-m^(3))+5(10k)^(1) (m^(4))+(10k)^(0)(-m^(5))`

∴
`(10k-m)^(5)=100000k^(5)-50000)k^(4)m+10000k^(3)m^(2)-1000k^(2)m^(3)+50km^(4)-m^(5)`