Combining like terms

Japanese school year: Junior high 1

What you learn

You will learn to identify terms with identical variable parts and combine them by adding or subtracting their coefficients. This fundamental skill is essential for simplifying complex expressions and solving algebraic equations. Prior knowledge of variables, coefficients, and operations with signed numbers will be helpful.

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Key points

Use this formula to combine like terms that share the exact same variable part. Add the numerical coefficients $a$ and $b$ together while keeping the variable $x$ .

ax + bx = (a + b)x

Use this formula to subtract like terms that share the same variable. Subtract coefficient $b$ from $a$ while retaining the common variable $x$ .

ax - bx = (a - b)x

Only terms that share both the exact same variables and identical powers, or constant numbers without variables, can be combined through addition or subtraction.

This inequality shows that terms with different powers are not like terms and cannot be combined. Even with the same variable $x$ , terms like $x^2$ and $x$ cannot be simplified into $x^3$ .

x^2 + x \neq x^3

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Practice 1Coming soon