Mathematics - Binomial Theorem Question with Solution | TestHub

Put $\sqrt{4x+1}=y$ and expand ${\left(\frac{1+y}{2}\right)}^7-{\left(\frac{1-y}{2}\right)}^7=\frac{2}{2^7}\left[{}^7{C}_{1}y+{}^7{C}_3{y}^3+{}^7{C}_5{y}^5+{}^7{C}_7{y}^7\right]$ Dividing by y leaves only the powers $y^0,y^2,y^4,y^6$, and $y^2=4x+1$ ⇒ the highest power is $(4x+1{)}^3\Rightarrow$ degree 3 in x.