To subtract $$(m^2 - 7mn - 3n^2)$$ from $$(m^2 + n^2)$$, first write the expression as $$(m^2 + n^2) - (m^2 - 7mn - 3n^2)$$. Distribute the subtraction by changing the sign of each term in the second polynomial to get $$m^2 + n^2 - m^2 + 7mn + 3n^2$$. Group the like terms together: $$m^2 - m^2 + 7mn + n^2 + 3n^2$$. Combine the like terms to get the final difference: $$7mn + 4n^2$$.

Claude

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 $$-10pq + 3q^2$$.

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

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OpenStax Intermediate Algebra

To subtract $$(a^2 + 5ab - 6b^2)$$ from $$(a^2 + b^2)$$, write the expression as $$(a^2 + b^2) - (a^2 + 5ab - 6b^2)$$. Distribute the subtraction by changing the sign of each term in the second polynomial to get $$a^2 + b^2 - a^2 - 5ab + 6b^2$$. Next, rearrange the terms to group the like terms together: $$a^2 - a^2 - 5ab + b^2 + 6b^2$$. Combine the like terms to find the difference: $$-5ab + 7b^2$$.

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