Factored to Standard Form Calculator
Input binomial factors and watch as the equation is synthesized into Standard Form, step-by-step, through a visual FOIL algorithm.
Factored Form Input
FOIL Synthesis
First
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Outer
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Inner
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Last
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Combine Outer + Inner
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Synthesized Standard Form
Ax² + Bx + C
Understanding the Forms
In algebra, the same quadratic equation can be written in different ways. This tool converts from Factored Form to Standard Form.
Factored Form
y = a(x - p)(x - q)
This form is incredibly useful because it immediately tells you the x-intercepts (or roots) of the parabola, which are at x = p and x = q.
Standard Form
y = Ax² + Bx + C
This is the most common form of a quadratic equation. It clearly shows the quadratic term (Ax²), the linear term (Bx), and the constant term (C), which is the y-intercept.
The FOIL Method Explained
FOIL is a mnemonic for the steps used to multiply two binomials. Our calculator visualizes this process in the "Synthesis Grid."
First
Multiply the first terms in each binomial. In (ax+b)(cx+d), this is (ax) × (cx).
Outer
Multiply the outermost terms. In (ax+b)(cx+d), this is (ax) × (d).
Inner
Multiply the innermost terms. In (ax+b)(cx+d), this is (b) × (cx).
Last
Multiply the last terms in each binomial. In (ax+b)(cx+d), this is (b) × (d).
Combine Like Terms
The final step is to add the results of the "Outer" and "Inner" steps together, as they are both linear terms (containing 'x'). This gives you the 'Bx' term in the standard form.
Key Features
This tool is more than a calculator; it's an interactive learning module designed for clarity and insight.
- Live Synthesis: All calculations update in real-time as you type, providing an instant feedback loop that reinforces the algebraic concepts.
- Visual FOIL Grid: The tool breaks down the multiplication into the four distinct FOIL steps, making the process transparent and easy to follow.
- Clear Combination Step: A dedicated panel shows exactly how the Outer and Inner terms are combined, a common point of confusion for students.
Frequently Asked Questions
Get quick answers to common questions about converting factored form to standard form.
Why do I need to convert to Standard Form?
While factored form is great for finding x-intercepts, standard form (Ax² + Bx + C) is essential for other key operations. For example, the coefficients A, B, and C are used directly in the Quadratic Formula to find the roots, and the formula -B / 2A gives you the x-coordinate of the parabola's vertex.
What if one of my factors is just a number?
If you have an equation like y = 3(x+2), this is not a product of two binomials, but a linear equation. To find its standard form, you would simply distribute the 3 to get y = 3x + 6. This calculator is specifically designed for multiplying two binomials (expressions with two terms).
Can I enter negative numbers?
Yes. To represent a factor like (2x - 5), you would enter 2 for 'a' and -5 for 'b'. The calculator handles negative numbers correctly in all steps of the FOIL process and will display the correct signs in the final standard form equation.
