1Cademy - Subtracting $$(c^2 - 4c + 7)$$ from $$(7c^2

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Procedure for Combining Like Terms

Example

Subtracting $(c^2 - 4c + 7)$ from $(7c^2 - 5c + 3)$

Subtract $(c^2 - 4c + 7)$ from $(7c^2 - 5c + 3)$ . The phrasing "subtract A from B" means the expression is written as $B - A$ , so the polynomial after the word "from" comes first:

$(7c^2 - 5c + 3) - (c^2 - 4c + 7)$

Step 1 — Distribute the subtraction and identify like terms: Multiply each term of the second polynomial by $-1$ : $-(c^2 - 4c + 7) = -c^2 + 4c - 7$ . The expression becomes:

$7c^2 - 5c + 3 - c^2 + 4c - 7$

The $c^2$ -terms are $7c^2$ and $-c^2$ ; the $c$ -terms are $-5c$ and $4c$ ; the constants are $3$ and $-7$ .

Step 2 — Rearrange the terms: Group like terms together:

$7c^2 - c^2 - 5c + 4c + 3 - 7$

Step 3 — Combine like terms: $7 - 1 = 6$ gives $6c^2$ ; $-5 + 4 = -1$ gives $-c$ ; $3 - 7 = -4$ .

The result is $6c^2 - c - 4$ .

This example reinforces two important points: the phrase "subtract A from B" reverses the reading order so that B is written first, and distributing the negative sign changes the sign of every term in the polynomial being subtracted — including turning $-4c$ into $+4c$ and $+7$ into $-7$ .

Updated 2026-04-21

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OpenStax Elementary Algebra

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