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Simplifying (p3−p2q)+(pq2+q3)−(p2q+pq2)(p^3 - p^2q) + (pq^2 + q^3) - (p^2q + pq^2)

To simplify the polynomial expression (p3−p2q)+(pq2+q3)−(p2q+pq2)(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: p3−p2q+pq2+q3−p2q−pq2p^3 - p^2q + pq^2 + q^3 - p^2q - pq^2. Next, rearrange the expression to group like terms together: p3−p2q−p2q+pq2−pq2+q3p^3 - p^2q - p^2q + pq^2 - pq^2 + q^3. Finally, combine the like terms. The terms −p2q-p^2q and −p2q-p^2q combine to −2p2q-2p^2q, and the terms +pq2+pq^2 and −pq2-pq^2 cancel out, resulting in the simplified polynomial: p3−2p2q+q3p^3 - 2p^2q + q^3.

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Updated 2026-06-18

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