The total number of terms in the expansion of $(x + a)^{47} - (x - a)^{47}$ after simplification is

${ \left( x+a \right) }^{ 47 }-{ \left( x-a \right) }^{ 47 }$

When we expand the above equation using binomial expansion

$(x +y)^{n} = \displaystyle (\sum_{k=0}^{n} {^{n}C_k} x^{k}y^{n-k})$

So the above equation becomes

$(x +a)^{47} = \displaystyle (\sum_{k=0}^{47} {^{47}C_k} x^{k}a^{47-k})$

$(x -a)^{47} = \displaystyle (\sum_{k=0}^{47} {^{47}C_k} x^{k}(-a)^{47-k})$

${ \left( x+a \right) }^{ 47 }\Rightarrow$There are 48 terms in the expansion and all are positive

${ \left( x-a \right) }^{ 47 }\Rightarrow$There are 48 terms in the expansion

The terms with odd powers of a will be cancelled and those with even powers of a will add up.

24 terms will be positive and 24 negative in the expansion of $(x-a)^{47}$

48 terms positive-[24 terms negative and 24 terms positive]

$=48\quad terms\quad positive +24\quad terms\quad negative+24\quad terms\quad positive$

$=24$ terms