1Cademy - Subtracting $$(p^2 + 10pq - 2q^2)$$ from $$(p^2 + q^2)$$

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Adding and Subtracting Polynomials

Example

Subtracting $(p^2 + 10pq - 2q^2)$ from $(p^2 + q^2)$

To subtract $(p^2 + 10pq - 2q^2)$ from $(p^2 + q^2)$ , first write the subtraction expression:
$(p^2 + q^2) - (p^2 + 10pq - 2q^2)$

Next, distribute the subtraction by multiplying each term in the second polynomial by $-1$ , which changes their signs:
$p^2 + q^2 - p^2 - 10pq + 2q^2$

Rearrange the terms to group the like terms together:
$p^2 - p^2 - 10pq + q^2 + 2q^2$

Finally, combine the like terms. The $p^2$ terms cancel out:
$-10pq + 3q^2$

The difference is $-10pq + 3q^2$ .

Updated 2026-04-29

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OpenStax Intermediate Algebra

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Intermediate Algebra @ OpenStax

Ch.5 Polynomials and Polynomial Functions - Intermediate Algebra @ OpenStax

Algebra

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