Polynomial Operations · Grades 10–10

Polynomial Operations Worksheets

Adding, subtracting, and multiplying binomials (the FOIL method and beyond) built from clean integer coefficients so every worked solution is exact.

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What it is

Polynomials add and subtract by combining like terms, the same as simplifying an expression. Multiplying two binomials uses FOIL (First, Outer, Inner, Last) to make sure every term in the first binomial multiplies every term in the second.

Why it matters

Polynomial arithmetic is the bridge between simplifying expressions and factoring: students who are fluent multiplying binomials recognize factored forms much faster, and struggle far less with the reverse process later.

How to do it

  1. For addition or subtraction: combine the x-terms together, then the constants together.
  2. For multiplication: multiply First terms, Outer terms, Inner terms, and Last terms (FOIL).
  3. Combine any like terms in the result to get the final answer.

Examples by level

  • Beginner(x − 6) + (4x + 3) =5x − 3
  • Intermediate(x + 6) − (3x − 5) =−2x + 11
  • Advanced(10x − 8)(6x − 3) =60x² − 78x + 24

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

  • Only multiplying the First and Last terms and skipping Outer/Inner.
  • Forgetting to distribute a negative sign to both terms when subtracting.
  • Not combining like terms in the final answer after multiplying.

Tips

  • When subtracting, distribute the negative sign to BOTH terms in the second binomial, not just the first.
  • FOIL always produces 4 terms before combining, if you're missing one, you likely skipped a pair.

For parents

FOIL is easy to say but easy to apply out of order, have your child physically draw arrows connecting each pair of terms before multiplying.

For teachers

Introduce addition and subtraction of binomials before multiplication; students who haven't internalized 'combine like terms' struggle with FOIL's final simplification step.

Key vocabulary

binomial
a polynomial with exactly two terms
FOIL
First, Outer, Inner, Last, the order for multiplying two binomials

Frequently asked questions

What grade are polynomial operations taught in?
Binomial addition, subtraction, and multiplication are introduced in Grade 10, right after linear equations and before factoring.
What does FOIL stand for?
First, Outer, Inner, Last, the four pairs of terms you multiply when expanding two binomials.

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