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.#

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