the first four term of the expansion : [tex](1+2x)^{-2}=1-4x+12x^{2}-32x^{3+...[/tex]
using the formula of expansion:
[tex](1+x)^{n}=1+nx+\frac{n(n-1)x^{2}}{2!}+\frac{n (n-1)(n-2)x^{3}}{3!} +......[/tex]
compare to the: [tex](1+2x)^{-2}[/tex]
[tex](1+2x)^{-2}=1+(-2)(2x)+\frac{(-2)(-3)(2x)^{2}}{2!}+\frac{(-2)(-3)(-4)(2x)^{3}}{3!}+...[/tex]
[tex]=1-4x+\frac{6*4x^{2}}2-\frac{24*8x^{3}}{6}+...[/tex]
[tex]=1-4x+12x^{2}-32x^{3+...[/tex]
the first four term of the expansion :[tex](1+2x)^{-2}=1-4x+12x^{2}-32x^{3+...[/tex]
learn more about expansion here:
https://brainly.com/question/5215508
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