1Cademy - Simplifying $$(p^3 - p^2q) + (pq^2 + q^3)

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Adding and Subtracting Polynomials

Example

Simplifying $(p^3 - p^2q) + (pq^2 + q^3) - (p^2q + pq^2)$

To simplify the polynomial expression $(p^3 - p^2q) + (pq^2 + q^3) - (p^2q + pq^2)$ , begin by distributing the addition and subtraction. The addition leaves signs unchanged, while the subtraction changes the signs of the terms in the final polynomial: $p^3 - p^2q + pq^2 + q^3 - p^2q - pq^2$ . Next, rearrange the expression to group like terms together: $p^3 - p^2q - p^2q + pq^2 - pq^2 + q^3$ . Finally, combine the like terms. The terms $-p^2q$ and $-p^2q$ combine to $-2p^2q$ , and the terms $+pq^2$ and $-pq^2$ cancel out, resulting in the simplified polynomial: $p^3 - 2p^2q + q^3$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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