Foil Method Calculator

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FOIL Method Calculator

First Binomial (ax + b):

Second Binomial (cx + d):

Result:

function calculateFoil() { var a = parseFloat(document.getElementById('a_coeff').value); var b = parseFloat(document.getElementById('b_const').value); var c = parseFloat(document.getElementById('c_coeff').value); var d = parseFloat(document.getElementById('d_const').value); var foilOutput = document.getElementById('foilOutput'); var foilSteps = document.getElementById('foilSteps'); if (isNaN(a) || isNaN(b) || isNaN(c) || isNaN(d)) { foilOutput.innerHTML = "Please enter valid numbers for all fields."; foilSteps.innerHTML = ""; return; } // FOIL Method Calculation // First var firstTermCoeff = a * c; var firstTerm = firstTermCoeff + "x²"; // Outer var outerTermCoeff = a * d; var outerTerm = outerTermCoeff + "x"; // Inner var innerTermCoeff = b * c; var innerTerm = innerTermCoeff + "x"; // Last var lastTerm = b * d; // Combine like terms var xTermCoeff = outerTermCoeff + innerTermCoeff; // Construct the final polynomial string var finalPolynomial = ""; if (firstTermCoeff !== 0) { finalPolynomial += firstTermCoeff + "x²"; } if (xTermCoeff !== 0) { if (xTermCoeff > 0 && finalPolynomial !== "") { finalPolynomial += " + "; } else if (xTermCoeff 0 && finalPolynomial !== "") { finalPolynomial += " + "; } else if (lastTerm < 0) { finalPolynomial += " "; // Add space for negative sign } finalPolynomial += lastTerm; } if (finalPolynomial === "") { finalPolynomial = "0"; // In case all terms cancel out } // Construct the steps string var stepsHtml = "

Steps:

"; stepsHtml += "Given binomials: (" + a + "x + " + b + ")(" + c + "x + " + d + ")"; stepsHtml += "First: (" + a + "x) * (" + c + "x) = " + firstTerm + ""; stepsHtml += "Outer: (" + a + "x) * (" + d + ") = " + outerTerm + ""; stepsHtml += "Inner: (" + b + ") * (" + c + "x) = " + innerTerm + ""; stepsHtml += "Last: (" + b + ") * (" + d + ") = " + lastTerm + ""; stepsHtml += "Combine: " + firstTerm + " + " + outerTerm + " + " + innerTerm + " + " + lastTerm + ""; stepsHtml += "Simplify: " + finalPolynomial + ""; foilOutput.innerHTML = "The product is: " + finalPolynomial + ""; foilSteps.innerHTML = stepsHtml; }

Understanding the FOIL Method

The FOIL method is a mnemonic used to remember the steps for multiplying two binomials. A binomial is a polynomial with two terms, such as (ax + b) or (cx + d). The FOIL acronym stands for First, Outer, Inner, Last, referring to the pairs of terms that need to be multiplied together.

What Does FOIL Stand For?

  • F – First: Multiply the first terms in each binomial.
  • O – Outer: Multiply the outer terms (the first term of the first binomial and the second term of the second binomial).
  • I – Inner: Multiply the inner terms (the second term of the first binomial and the first term of the second binomial).
  • L – Last: Multiply the last terms in each binomial.

How the FOIL Method Works (Step-by-Step Example)

Let's take an example: Multiply (x + 3) by (2x + 5).

  1. First: Multiply the first terms of each binomial.

    2. (x) * (2x) = 2x²

  2. Outer: Multiply the outermost terms.

    3. (x) * (5) = 5x

  3. Inner: Multiply the innermost terms.

    4. (3) * (2x) = 6x

  4. Last: Multiply the last terms of each binomial.

    5. (3) * (5) = 15

  5. Combine and Simplify: Add all the products together and combine any like terms.

    6. 2x² + 5x + 6x + 15

    2x² + 11x + 15

So, (x + 3)(2x + 5) = 2x² + 11x + 15.

Using the Calculator

Our FOIL Method Calculator simplifies this process. Simply input the coefficients and constant terms for your two binomials (ax + b) and (cx + d):

  • Coefficient of x (a): The number multiplying 'x' in the first binomial.
  • Constant Term (b): The standalone number in the first binomial.
  • Coefficient of x (c): The number multiplying 'x' in the second binomial.
  • Constant Term (d): The standalone number in the second binomial.

Click "Calculate FOIL," and the calculator will instantly display the expanded polynomial and show you the step-by-step breakdown of the First, Outer, Inner, and Last multiplications, making it easy to understand how the final result is achieved.

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