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Here are some tips for Simplifying Algebraic Expressions, which aligns with New York state standards:

Simplifying Algebraic Expressions


To review algebraic terms, see here.

Simplify algebraic expressions by combining like terms.
Like terms are terms with the same variable or variables.

Like termsUnlike terms
All constants are like terms. Constants and variables are not like terms.
2, -34, 0.59, ¼ 18, x
All these terms have one variable, y. Terms with different variables are not like terms.
3y, -10y, y, 6y 7x, 7y
All these terms have the same variable, t3. Terms with the same variable but different exponents are not like terms.
t3, 9t3, ½t3, -14t3 10y, 3y2
All these terms have the same variable combination, xy. Terms with different variable combinations are not like terms.
29xy, 0.5xy, xy, -xy x, 8xy


Example 1: One variable

-x - 6 + 5x   Simplified:

-x and 5x are like terms, so combine them.
-x - 6 + 5x = 4x - 6

The answer is


Example 2: Two variables

3y + 4 - y + 4x - 6   Simplified:

Combine the x and y terms and the constants.
3y + 4 - y + 4x - 6 =
4x + (3y - y) + (4 - 6) =
4x + 2y + -2 =
This simplifies to 4x + 2y - 2

The answer is


Example 3:

Simplify the expression and order your answer based on alphabetical letter and magnitude.
4x2 - 3y + x - 2x2 - 2 - 3y + 7   Simplified:

Combine the terms and simplify.
4x2 - 3y + x - 2x2 - 2 - 3y + 7 =
(4x2 - 2x2) + x + (-3y - 3y) + (-2 + 7) =
2x2 + x + (-6y) + 5 =
This simplifies to 2x2 + x - 6y + 5

The answer is

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