Core Algebra Skills

Properties of Exponents

• Product Rule: \( x^a \cdot x^b = x^{a+b} \)
• Quotient Rule: \( \frac{x^a}{x^b} = x^{a-b} \)
• Power Rule: \( (x^a)^b = x^{a \cdot b} \)
• Zero and Negative Exponents: \( x^0 = 1 \), \( x^{-a} = \frac{1}{x^a} \)

Combining Like Terms

• Add or subtract polynomials by combining like terms.

Factoring

• GCF extraction
• Trinomials: \( ax^2 + bx + c \)
• Factoring by grouping
• Difference of squares: \( a^2 - b^2 = (a - b)(a + b) \)

Expanding

• Distributive property: \( a(b + c) = ab + ac \)
• Squaring binomials: \( (a + b)^2 = a^2 + 2ab + b^2 \)
• Cubing binomials and using special product formulas

Rational Expressions

• Simplify by factoring
• Use common denominators
• Find undefined values in the denominator

Radicals & Fractional Exponents

• \( \sqrt[n]{x} = x^{1/n} \)
• Simplify square and cube roots
• Rationalize denominators

Absolute Value

• Simplify and evaluate absolute value expressions
• Understand absolute value in equations and inequalities

Word Problem Translation

• Convert verbal statements into algebraic expressions
• Recognize equivalent forms in context (e.g., interest growth)

Functions and Substitution

• Substitute and simplify expressions inside functions
• Examples: \( f(x) + g(x) \), \( f(g(x)) \)

Algebraic Properties

• Commutative: \( a + b = b + a \), \( ab = ba \)
• Associative: \( (a + b) + c = a + (b + c) \)
• Distributive: \( a(b + c) = ab + ac \)

SAT Strategies

• Recognize common answer patterns
• Match different forms (factored vs. expanded)
• Simplify to match multiple choice answers
• Identify structure to spot equivalency
• Avoid common mistakes (exponent rules, factoring errors, sign errors)