Quick answer

Rewrite P − Q as P + (−Q). Flip every sign in Q, then combine like terms.

Formula

  • (P − Q)(x) = Σ (a_k − b_k) x^k

Introduction

Subtraction errors usually mean a sign never reached a term in Q(x). The examples below show correct distribution before you use polynomial calculator Subtract mode.

Work slowly through parentheses; speed without distribution is what costs points.

Sign distribution

Parentheses around Q matter when Q has more than one term. The minus applies to each addend inside: −(a + b) = −a − b.

Follow the step list in how to subtract polynomials alongside these numeric templates.

Notice how P − Q differs from Q − P in polynomial addition vs subtraction when the same expressions swap order.

Worked pattern

  • Step 1: Negate every term of Q(x).
  • Step 2: Add P(x) and −Q(x) by aligning powers.
  • Step 3: Simplify and write standard form.

Double negatives become positives: subtracting −2x is adding 2x. Mark sign changes in a different color on paper if that helps.

Binomial minus binomial problems are good drills before cubics because there are fewer columns but the same sign rules. Moreover, you can try this app that can help with related math.

Step-by-step guide

  1. Parenthesize Q(x) before flipping signs. Write P − ( … all terms of Q … ). Only then distribute the minus across each term.
  2. Combine like terms. Use the addition layout on P and −Q. Pad missing powers with zero.
  3. Verify order and simplify. Confirm you computed P − Q, not Q − P. Drop zero terms unless the answer is 0.
  4. Compare with the calculator. Subtract mode in polynomial calculator should match your final R(x).

Example: quadratic subtraction

(3x² + 5) − (x² − 2). Distribute: 3x² + 5 − x² + 2. Combine x²: 3 − 1 = 2. Constants: 5 + 2 = 7.

Result: 2x² + 7. The x terms were absent (coefficient 0) on both sides.

Enter coefficients for both quadratics in polynomial calculator Subtract mode to verify.