I have an expression, say for instance $\rm{expression}=7+2a(x+1)^2+3a^4(y-2)(x+5)$. I would like to further multiply this expression by $a$ and I aim for a result of the form $7a+2a^2(x+1)^2+3a^5(y-2)(x+5)$. However, when I do $a*$ the expression, it generates $a[7+2a(x+1)^2+3a^4(y-2)(x+5)]$ which did not penetrate that $a$ into the original expression. On the other hand, if I do $\rm{Expand[a*(7+2a(x+1)^2+3a^4(y-2)(x+5))]}$, it generates $7a+2 a^2 - 30 a^5 + 4 a^2 x - 6 a^5 x + 2 a^2 x^2 + 15 a^5 y + 3 a^5 x y$ which corresponds to a full expansion.

All I need is to rise exponents of $a$ in the original expression by one, so $a^n$ becomes $a^{n+1}$ for all $n\geq 0$, while holding all other terms stay unchanged. How could I implement that?

Note: I also tried the replacement-type command ${\rm{expression}}/.a^n\to a^{n+1}$, but it only rises those exponents greater than 1, namely I got $7+2 a (1 + x)^2 + 3 a^5 (5 + x) (-2 + y)$.

  • $\begingroup$ These are all equivalent forms, what's the point? $\endgroup$ – yarchik Mar 13 at 22:42
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    $\begingroup$ Use Distribute, e.g., Distribute[a * expression]. Also, you should provide copyable plaintext to make life easier for people answering your question. $\endgroup$ – Carl Woll Mar 13 at 22:52
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    $\begingroup$ Have you seen Collect ? $\endgroup$ – LouisB Mar 13 at 22:53

Try this:

p[x_,y_, a_] := 7 + 2 a (x + 1)^2 + 3 a^4 (y - 2) (x + 5)
Collect[a*p[x, y, a], a, FullSimplify]

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