How do you expand #(1-2b^4)^5#?

1 Answer
Ratnaker Mehta
Jul 7, 2016

#:. (1-2b^4)^5=1-10b^4+40b^8-80b^12+80b^16-32b^20.#

Explanation:

Binomial Theorem states that,
#(1+x)^n=""_nC_0x^0+""_nC_1x+""_nC_2x^2+""_nC_3x^3+...+""_nC_rx^r+...+""_nC_nx^n#

Letting #n=5, x=-2b^4,#

#(1-2b^4)^5=""_5C_0+""_5C_1(-2b^4)+""_5C_2(-2b^4)^2+""_5C_3*(-2b^4)^3+""_5C_4(-2b^4)^4+""_5C_5(-2b^4)^5#

In this, #""_5C_0=""_5C_5=1, ""_5C_1=""_5C_4=5,""_5C_2=""_5C_3=(5*4)/(1*2)=10.#

#:. (1-2b^4)^5=1+5(-2b^4)+10(4b^8)+10(-8b^12)+5(16b^16)+(-32b^20)#
#=1-10b^4+40b^8-80b^12+80b^16-32b^20.#

Was it helpful?then, Enjoy Maths.!

Related questions
See all questions in Pascal's Triangle and Binomial Expansion
Impact of this question
1306 views around the world
You can reuse this answer
Creative Commons License