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Multiply (ax + b)(cx + d)
First Binomial (Top)
(
x
+
)
Second Binomial (Left)
(
x
+
)
1x
3
1x
x²
3x
-2
-2x
-6
Combined Result
x² + x - 6
How to Use This Calculator
1
Enter Values
Fill in the required fields with your numbers.
2
Calculate
Click calculate or see results update in real time.
3
Read Results
View detailed breakdowns and explanations below.
📘 Formula Used
The Box Method is an alternative to FOIL. It computes four products:
(ax)(cx) = acx²
(b)(cx) = bcx
(ax)(d) = adx
(b)(d) = bd
(b)(cx) = bcx
(ax)(d) = adx
(b)(d) = bd
Summing them gives: acx² + (bc + ad)x + bd
🧠 How It Works
- Draw a 2x2 Grid: Place the terms of the first binomial on top, and the second on the left.
- Multiply Into Cells: Fill each cell by multiplying the term above it by the term to its left.
- Add Diagonals: The top-right and bottom-left cells usually contain "x" terms that can be added together.
✍️ Worked Example
Multiply: (x + 3)(x - 2)
- Top Left: x · x = x²
- Top Right: 3 · x = 3x
- Bottom Left: -2 · x = -2x
- Bottom Right: 3 · -2 = -6
Combine:
x² + (3x - 2x) - 6 = x² + x - 6
✅ Key Takeaways
- Visual method reduces arithmetic errors.
- Works for larger polynomials too (e.g. 3x3 grids for trinomials).
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