Advanced Math / Equivalent Expressions
Equivalent Expressions
Equivalent expressions have the same value for every allowed value of the variable. Common strategies include expanding, factoring, combining like terms, applying exponent rules, completing the square, and simplifying rational expressions while respecting denominator restrictions.
Least you need to know
- Special products such as difference of squares and perfect-square trinomials can make rewriting faster.
- Rational expressions can be simplified by canceling common factors, not individual terms.
Key notation
- $a^2-b^2$ — A difference of squares, equal to $(a-b)(a+b)$
Worked example
- Factor or expand as needed.
- Compare coefficients or simplify common factors.
Common mistakes
- Do not cancel terms separated by addition or subtraction.
- A negative exponent means a reciprocal.
How to recognize it
- The problem asks which expression is equivalent.
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