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java - Regular expression for arithmetic expression

I,m trying to write a regex to check if the given string is like a + b, 2 + a + b, 3 + 6 * 9 + 6 * 5 + a * b, etc...

Only + and * operators.

I tried

if (str.matches("(\d|\w \+|\*){1,} \d|\w"))

Unfortunately it only handles cases like 3 * 7 ... (numeric * numeric).

Waiting for your answers, thanks for reading me.

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Put * and + inside a character class.

str.matches("\w(?:\s[+*]\s\w)+");

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