**G**iven (1+x)^43 is the binomial term :

and terms in the binomial expansion are r+2 and 2r+1

using the **General formula ** Tr+1=^{n} C_{r}_{ }* a^{n-r} b^{r }

here term=(2r+1)

so r in the above formula will be: 2r

Now expand using 2r and we get ^{n}C_{2r}_{ }*1^{43-2r} *x^{2r}

now doing the same for the r+2^{th} term we have ^{n}C_{r}_{+1} * 1 ^{43-r+1} * x^{r}^{+1}

Note 1^{n} =1 (meaning 1 raise to any number is 1)or(1*1*1*1*1......n=1)

so we know 1^{43-2r} and 1^{43-r+1} are both equal to one.

Given the 2r+1 and r+2 terms are equal

we can equate them

^{n}C_{2r}_{ }*1^{43-2r} *x^{2r }= ^{n}C_{r}_{+1} * 1 ^{43-r+1} * x^{r+1 }

^{n}C_{2r} *x^{2r }= ^{n}C_{r}_{+1}* x^{r+1}

Now we know the powers of x will be as the terms are equal

hence we equate the x terms(without coefficients)

x^{2r}^{ }=x^{r+1 as they have the same base when x divides the exponents will only subtract (}x^{2r /}x^{r+1)}

so x^{2r-r}=x^{1}

hence x^{r}=x^{1}

and r=1