1Cademy - Simplifying $$4(x - 8) - (x + 3)$$ by Distributing and Combining Like Terms

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Simplifying $4(x - 8) - (x + 3)$ by Distributing and Combining Like Terms

Simplify $4(x - 8) - (x + 3)$ — an expression that contains two sets of parentheses, each requiring distribution before the terms can be combined.

Step 1 — Distribute both factors: Apply the distributive property to each parenthesized group. For the first group, multiply $4$ by each term: $4 \cdot x = 4x$ and $4 \cdot (-8) = -32$ . For the second group, the subtraction sign in front of $(x + 3)$ acts as multiplication by $-1$ : $-1 \cdot x = -x$ and $-1 \cdot 3 = -3$ :

$4x - 32 - x - 3$

Step 2 — Combine like terms: Group the variable terms and the constant terms. The $x$ -terms are $4x$ and $-x$ : $4x - x = 3x$ . The constants are $-32$ and $-3$ : $-32 - 3 = -35$ :

$3x - 35$

The simplified result is $3x - 35$ . The key insight is that a subtraction sign immediately before a set of parentheses is equivalent to multiplying everything inside by $-1$ , which changes the sign of every term. This is why $-(x + 3)$ becomes $-x - 3$ rather than $-x + 3$ .

Updated 2026-05-02

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