Expansion and Factorization Calculator
Expand (ax+b)(cx+d) using four products, or factor a monic quadratic x²+Bx+C over the integers. See how the middle terms combine.
YOUR CALCULATION
Result
—
Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Expansion multiplies every term in the first bracket by every term in the second bracket, then combines the two x terms. Integer factorization of x²+Bx+C looks for integers p and q with p+q=B and pq=C.
(ax+b)(cx+d)=acx²+(ad+bc)x+bd; x²+Bx+C=(x+p)(x+q) when p+q=B and pq=C
Worked example
(2x+3)(x−4)=2x²−8x+3x−12=2x²−5x−12. Separately, x²−5x+6=(x−2)(x−3), because −2+(−3)=−5 and (−2)(−3)=6.
Assumptions and input details
Expansion accepts integer a,b,c,d within ±10,000 and also handles zero coefficients. Factorization accepts integer B,C within ±1e6 and is restricted to monic quadratics with leading coefficient 1. A failure to find an integer factor pair does not mean the equation has no real or complex roots; the linked quadratic equation tool solves those cases. Factoring an expression does not solve an equation unless the expression is set equal to zero.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Integer coefficients, products and factor pairs are exact within the stated limits. No decimal-coefficient or symbolic-variable factorization is implied.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
Solve ax² + bx + c = 0, including real, repeated and complex roots. Inspect the discriminant, worked steps and the function graph.
Solve ax+b=cx+d with whole numbers, decimals or fractions. Follow the same operation on both sides and check the answer by substitution.
Add, subtract, multiply or divide fractions and mixed numbers. Follow exact fraction steps, simplification and a number-line diagram.
Reserved advertising space.