How do you use the Binomial Theorem to find the value of 99^4994? Precalculus The Binomial Theorem The Binomial Theorem 1 Answer maganbhai P. May 3, 2018 99^4=96059601994=96059601 Explanation: We know that, color(blue)((x+a)^n=nC_0x^n+nC_1x^(n-1)a+nC_2x^(n- 2)a^2+...+nC_na^n Now, 99^4=(100-1)^4=(100+(-1))^4, Take , color(blue)(x=100 , a=-1 and n=4 99^4=4C_0(100)^4+4C_1(100)^3(-1)+4C_2(100)^2(-1)^2+4C_ 3(100)^1(-1)^3+4C_4 (-1)^4 Here, 4C_0=1,4C_1=4,4C_2=(4xx3)/(2xx1)=6,4C_3= (4xx3xx2)/(3xx2xx1)=4 ,4C_4=1and 100=10^2 =>99^4=1(10^8)-4(10^6)+6(10^4)-4(10^2)+1 =>99^4=100000000-4000000+60000-400+1 =>99^4=100060001-4000400 =>99^4=96059601 Answer link Related questions What is the binomial theorem? How do I use the binomial theorem to expand (d-4b)^3? How do I use the the binomial theorem to expand (t + w)^4? How do I use the the binomial theorem to expand (v - u)^6? How do I use the binomial theorem to find the constant term? How do you find the coefficient of x^5 in the expansion of (2x+3)(x+1)^8? How do you find the coefficient of x^6 in the expansion of (2x+3)^10? How do you use the binomial series to expand f(x)=1/(sqrt(1+x^2))? How do you use the binomial series to expand 1 / (1+x)^4? How do you use the binomial series to expand f(x)=(1+x)^(1/3 )? See all questions in The Binomial Theorem Impact of this question 11837 views around the world You can reuse this answer Creative Commons License