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There are a couple of ways to interpret your problem, but all involve adding like terms.

A polynomial in one variable is the sum of monomials. Each monomial will have a coefficient and some power of the variable. A polynomial in multiple variables is the sum of terms. There are...

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There are a couple of ways to interpret your problem, but all involve adding like terms.

A polynomial in one variable is the sum of monomials. Each monomial will have a coefficient and some power of the variable. A polynomial in multiple variables is the sum of terms. There are some differences in definitions of these words (see link).

In a lower-level algebra class, when we say "add/subtract like terms," we generally mean terms with the same variables to the same powers.

So, `2x^2+3x^2=5x^2` ; can be shown using the distributive property:

`2x^2+3x^2=(2+3)x^2=5x^2`

Also, `2x^2y+3x^2y=5x^2y` (by the same reasoning).

However, in the case `2x^2y+3xy `, we cannot add the summands, as they are not like terms; the power on x is different. We can factor out a common xy to get `(2x+3)xy` to write it as a single entity, but we cannot add them.

(1) Taking your problem exactly as written:

3s2t-2st2+s2t ; multiplication is commutative, so we get 6st-4st+2st by multiplying the numerical factors in each term. Now the terms are like terms, and we can add/subtract the coefficients to get 4st.

(2) If you meant `3s^2t-2st^2+s^2t`, we note that the first and last term are like terms, so we can add their coefficients (the coefficient in the last term is an understood 1) to get `4s^2t-2st^2` . These terms are not like terms, so we cannot add them. We can factor them to get `2st(2s-t)`.

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