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Simplifying Expressions

Collect like terms to write an expression in its shortest correct form.

Collecting Like Terms

To simplify an expression, add or subtract the coefficients of like terms. Unlike terms are simply left as they are, written next to the others.

Example 1 — easy numbers

Simplify 3 x + 5 x . 1 Both terms have just x, so they are like terms. 2 Add the coefficients: 3 + 5 = 8 3 3 x + 5 x = 8 x Answer: 8 x

Example 2 — with subtraction

Simplify 7 y - 2 y + 4 y . 1 All three terms are like terms (all just y). 2 Combine the coefficients left to right: 7 - 2 + 4 = 9 3 7 y - 2 y + 4 y = 9 y Answer: 9 y

Example 3 — two different letters

Simplify 5 a + 3 b - 2 a + b. 1 Group the a-terms: 5 a - 2 a = 3 a 2 Group the b-terms: 3 b + b = 4 b 3 Write the results together: 3 a + 4 b Answer: 3 a + 4 b

Example 4 — with a squared term

Simplify 4 x^{2} + 3 x - x^{2} + 5 x . 1 Group the x^{2} -terms: 4 x^{2} - x^{2} = 3 x^{2} 2 Group the x -terms: 3 x + 5 x = 8 x 3 Write the results together: 3 x^{2} + 8 x Answer: 3 x^{2} + 8 x

Practice

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Simplify 6 m - 4 m + m .

Simplify 8 p - 3 q - 2 p + 5 q, then enter the coefficient of p in your answer.

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