How can I replace small expressions in larger expressions?
Simple example
Replace[a^2 + b^2 + 2*a*b + x, (a + b)^2 -> c]
I want to get c + x but the output is a^2 + b^2 + 2*a*b + x.
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2 Answers
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Try this.
First:
s = Solve[(a + b)^2 == c, a][[1, 1]]
(* a -> -b - Sqrt[c] *)
second:
a^2 + b^2 + 2*a*b + x /. s // Simplify
(* c + x *)
Have fun!
answered Jan 13, 2021 at 22:26
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A simple method:
a^2 + b^2 + 2*a*b + x /. Expand[(a + b)^2 -> c]
answered Feb 12, 2021 at 23:49
A little mouse on the pampasA little mouse on the pampas
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Replacedoes only literal replacements. TrySimplify[a^2 + b^2 + 2*a*b + x, Assumptions -> (a + b)^2 == c]instead. $\endgroup$Last@PolynomialReduce[a^2 + b^2 + 2*a*b + x, {(a + b)^2 - c}, {a, b, c, x}]. (The goal ofPolynomialReduceis not replacement, and, while it works here, it may not work in every instance. OTOH, depending on what the general goal is, if there is a more general goal, it may be more appropriate than replacement, since it is a quite common algebraic operation.) With a similar caveat, there's alsoFirst@GroebnerBasis[{a^2 + b^2 + 2*a*b + x, (a + b)^2 - c}, {c, x}, {a, b}]$\endgroup$