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Yup — here’s your Algebra 2 Identities & Formulas restructured into flashcard-ready format: super clean, categorized, and easy to plug into any app like Anki, Quizlet, Knowt, or Brainscape.

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1. Factoring Formulas & Identities

Q: What is the difference of squares formula?

A: a^2 - b^2 = (a - b)(a + b)

Q: What is the perfect square trinomial formula for a^2 + 2ab + b^2?

A: a^2 + 2ab + b^2 = (a + b)^2

Q: What is the perfect square trinomial formula for a^2 - 2ab + b^2?

A: a^2 - 2ab + b^2 = (a - b)^2

Q: What is the sum of cubes formula?

A: a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Q: What is the difference of cubes formula?

A: a^3 - b^3 = (a - b)(a^2 + ab + b^2)

Q: How do you factor by grouping?

A: Group like terms:

Example: ax + ay + bx + by = a(x + y) + b(x + y) = (a + b)(x + y)

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2. Quadratic Formulas & Functions

Q: What is the quadratic formula?

A: x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Q: How do you find the vertex of a parabola in standard form?

A: Use x = \frac{-b}{2a}, then plug in x to get y.

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3. Exponents & Radicals

Q: What is the product rule for exponents?

A: x^a \cdot x^b = x^{a + b}

Q: What is the quotient rule for exponents?

A: \frac{x^a}{x^b} = x^{a - b}

Q: What is the power rule for exponents?

A: (x^a)^b = x^{ab}

Q: What does a negative exponent mean?

A: x^{-a} = \frac{1}{x^a}

Q: What does zero exponent equal?

A: x^0 = 1, as long as x \neq 0

Q: What does a fractional exponent represent?

A: x^{a/b} = \sqrt[b]{x^a} = (\sqrt[b]{x})^a

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4. Logarithms

Q: What is the definition of a logarithm?

A: If b^y = x, then \log_b x = y

Q: What is the product rule for logarithms?

A: \log_b (MN) = \log_b M + \log_b N

Q: What is the quotient rule for logarithms?

A: \log_b \left(\frac{M}{N}\right) = \log_b M - \log_b N

Q: What is the power rule for logarithms?

A: \log_b (M^p) = p \cdot \log_b M

Q: What is the change of base formula?

A: \log_b M = \frac{\log_c M}{\log_c b}

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5. Absolute Value

Q: How do you solve an equation like |ax + b| = c?

A: Solve two cases: ax + b = c or ax + b = -c

Q: How do you solve |ax + b| < c?

A: Convert to compound inequality: -c < ax + b < c

Q: How do you solve |ax + b| > c?

A: Solve two separate cases: ax + b > c or ax + b < -c

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6. Complex Numbers

Q: What is the standard form of a complex number?

A: a + bi

Q: What is i?

A: i = \sqrt{-1} and i^2 = -1

Q: How do you find the absolute value (modulus) of a complex number?

A: |a + bi| = \sqrt{a^2 + b^2}