Algebra rules and equation-solving shortcuts commonly tested on the GMAT quant section. Front: the concept or rule. Back: definition or formula with a brief usage note.
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- Distributive property: a(b + c) = ?
- ab + ac. Use to expand products and factor expressions.
- FOIL method: (a + b)(c + d) = ?
- ac + ad + bc + bd. First, Outer, Inner, Last.
- Difference of squares: a^2 - b^2 = ?
- (a + b)(a - b). Factors as sum times difference.
- Perfect square trinomial: (a + b)^2 = ?
- a^2 + 2ab + b^2. First squared, double product, last squared.
- Sum of cubes: a^3 + b^3 = ?
- (a + b)(a^2 - ab + b^2). Factor as sum times a special trinomial.
- Difference of cubes: a^3 - b^3 = ?
- (a - b)(a^2 + ab + b^2). Factor as difference times a special trinomial.
- Quadratic formula: x = ?
- (-b +/- sqrt(b^2 - 4ac)) / 2a for ax^2 + bx + c = 0.
- Completing the square: what is the goal?
- Rewrite ax^2 + bx + c as (x + p)^2 + q to solve or analyze the quadratic.
- When you multiply or divide an inequality by a negative number, what happens to the sign?
- The inequality sign flips. If a < b and c < 0, then ac > bc.
- For a quadratic ax^2 + bx + c with roots r and s, the sum r + s = ?
- -b/a. The sum of roots equals negative b divided by a.
- For a quadratic ax^2 + bx + c with roots r and s, the product rs = ?
- c/a. The product of roots equals c divided by a.
- What is an extraneous solution?
- A value that satisfies the transformed equation but not the original equation, often from squaring both sides.
- Fraction addition: a/b + c/d = ?
- (ad + bc) / bd. Find a common denominator, add numerators.
- Fraction subtraction: a/b - c/d = ?
- (ad - bc) / bd. Find a common denominator, subtract numerators.
- Fraction multiplication: a/b * c/d = ?
- ac / bd. Multiply numerators together, multiply denominators together.