Combining Like Terms and the Distributive Property

Learn combining like terms, distributive property.

Lesson 3 of 32 parts Practice Flashcards

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Combining Like Terms

Objective: Explain combining like terms, apply the stated method, and check its conditions.

Like terms have identical variable parts, including exponents. Add or subtract their coefficients while preserving that variable part. A constant term is not like an x term, and x and x² cannot be combined into one x coefficient. Matching variables must also have matching exponents.

Formulas

$ax+bx=(a+b)x$

Worked examples

Try itCombine 6x+7x−7. What is the x coefficient?Show answer

Step 1: The x terms are like terms; the constant is separate. Step 2: Add their coefficients 6+7. Step 3: The coefficient is 13.

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Combining Like Terms

Objective: Explain combining like terms, apply the stated method, and check its conditions.

Formulas

$ax+bx=(a+b)x$

Worked examples

Try itCombine 6x+7x−7. What is the x coefficient?Show answer

Step 1: The x terms are like terms; the constant is separate. Step 2: Add their coefficients 6+7. Step 3: The coefficient is 13.

Distributive Property

Objective: Explain distributive property, apply the stated method, and check its conditions.

For real numbers a,b,c, a(b+c)=ab+ac. A factor outside parentheses multiplies every term inside. Distribution changes the expression’s form while preserving its value; an outside negative must be distributed to each term too. Distribute to every term, not only the first.

Formulas

$a(b+c)=ab+ac$

Worked examples

Try itFind the x coefficient after expanding 6(x+7).Show answer

Step 1: Multiply each term inside the parentheses. Step 2: The result is 6x+42. Step 3: The x coefficient is 6.

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