Q. Simplify the expression \( 2(10) + 2(x – 4) \)

Answer

We want to simplify the expression \(2(10) + 2(x – 4)\).

Step 1 — Apply the distributive property to each product.

Multiply 2 by 10 and distribute 2 across the parentheses \(x – 4\). This gives

\[
2(10) + 2(x – 4) = 20 + (2x – 8)
\]
Step 2 — Remove parentheses and collect like terms.

Remove the parentheses and group the constant terms \(20\) and \(-8\) together with the term containing \(x\):

\[
20 + 2x – 8 = 2x + (20 – 8)
\]

Compute the constant sum \(20 – 8 = 12\):

\[
2x + 12
\]
Step 3 — Optional: factor a common factor.

Both terms \(2x\) and \(12\) share a common factor 2, so you can factor 2 if desired:

\[
2x + 12 = 2(x + 6)
\]

Final simplified form: \(2x + 12\). Factored form (optional): \(2(x + 6)\).

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Distribute and combine like terms: 20 + 2x - 8 = 2x + 12.

The distributive property: a(b + c) = ab + ac. Here 2 multiplies both 10 and each term inside (x - 4).

Combine constants 20 and -8 to get 12; the 2x term is different type (variable) so it stays separate: 2x + 12.

Yes. Factor out 2: 2x + 12 = 2(x + 6).

Forgetting to distribute 2 to both terms, or mishandling the negative sign inside parentheses, e.g., doing 2(10) + 2x - 4 instead of 2x - 8.

Substitute value for x into both the original and simplified expressions; they should give the same result (e.g., x = 3 gives 18 in both).

2(10) + 2(3 - 4) = 20 + 2(-1) = 20 - 2 = 18.

Yes: evaluate parentheses first, then multiplication (distribute), then addition/subtraction. That guides distributing 2 before combining terms.

All real numbers; it's linear expression with no restrictions.

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