What is the simplified form of r + 3(s + 7r)?

What is the simplified form of r + 3(s + 7r)?

• A. 23r + 3s
• B. r + 3s + 21r
• C. 22r + 3s
• D. 3s + 7r

Answer: (C)

Distributive property and combining like terms are being tested. Distribute the 3 across the parentheses: 3(s + 7r) becomes 3s + 21r. So the expression becomes r + 3s + 21r. Now combine the r terms: r + 21r equals 22r. Thus the simplified form is 22r + 3s (order can also be 3s + 22r since order doesn’t matter). For a quick check, plug in values e.g., r = 2 and s = 1: original gives 2 + 3(1 + 14) = 2 + 45 = 47, and the simplified form gives 22·2 + 3·1 = 44 + 3 = 47, which matches. An intermediate form like r + 3s + 21r is technically equivalent but not fully simplified because the r terms can be combined into 22r. A form like 3s + 7r would omit the distribution of 3 to the 7r term, so it’s missing part of the expression.

Distributive property and combining like terms are being tested. Distribute the 3 across the parentheses: 3(s + 7r) becomes 3s + 21r. So the expression becomes r + 3s + 21r. Now combine the r terms: r + 21r equals 22r. Thus the simplified form is 22r + 3s (order can also be 3s + 22r since order doesn’t matter).

For a quick check, plug in values e.g., r = 2 and s = 1: original gives 2 + 3(1 + 14) = 2 + 45 = 47, and the simplified form gives 22·2 + 3·1 = 44 + 3 = 47, which matches.

An intermediate form like r + 3s + 21r is technically equivalent but not fully simplified because the r terms can be combined into 22r. A form like 3s + 7r would omit the distribution of 3 to the 7r term, so it’s missing part of the expression.