Simplifying Expressions
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Algebra
Summary
Simplifying algebraic expressions on the ACT depends on recognizing like terms, combining only terms with identical variable parts, and handling parentheses correctly during addition and subtraction. Strong simplification habits help turn complicated expressions into clean final forms without changing their value.
- Simplification means rewriting one expression as an equivalent expression, such as turning 3x + 5x into 8x, which works because the terms are like terms and their coefficients can be added.
- Like terms have the same variable part and may differ only in coefficient, so expressions such as 15y - 8y and 3y^2 + 3y^2 can be simplified by adding or subtracting the coefficients.
- Terms with different variables or different exponents cannot be combined, so expressions with multiple powers of the same variable must be grouped carefully before simplifying.
- Multiplication is commutative, so variable order does not matter: xy and yx represent the same variable part, which means terms that look different at first may still be like terms.
- When a plus sign appears before parentheses, the parentheses can be removed directly; when a minus sign appears before parentheses, every sign inside must be reversed before combining like terms.
Chapters
00:00
Combining Like Terms
01:58
Recognizing When Terms Can and Cannot Combine
02:36
Using Commutative Multiplication to Spot Like Terms
04:07
Removing Parentheses After Addition
04:48
Distributing a Negative Sign Across Parentheses