Math guides

Worked examples for the algebra topics where students most often lose points. Each guide shows every step, the common mistake, and the exact line where it happens, with practice problems and answers at the end. Written for students, and for parents helping with homework.

• Completing the square, step by step

  Solve a quadratic or find vertex form by building a perfect square, including what to do when the x² term has a coefficient.

• Factoring trinomials when a ≠ 1 (the AC method)

  Factor ax² + bx + c by splitting the middle term and grouping, and spot the sign slip that makes the groups not match.

• Why (a + b)² isn't a² + b² — and other distribution mistakes

  Why the middle term matters, shown with numbers and a picture, plus the minus-sign and square-root versions of the same mistake.

• Solving equations with fractions: clear the denominators first

  Multiply every term by the least common denominator, then solve an equation with no fractions in it. Includes the term people forget to multiply.

• Flipping the inequality sign: when and why

  Flip only when you multiply or divide by a negative. Why that's the rule, and the two ways students flip when they shouldn't.

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