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Square Trinomial Calculator Online

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The Square Trinomial Calculator helps you quickly and accurately expand and simplify trinomials of the form (a + b + c)^2. This tool is designed to save time and reduce errors in manual calculations, making it easier for students, teachers, and professionals to handle mathematical problems involving square trinomials.

Formula of Square Trinomial Calculator

To calculate the square of a trinomial, use the following formula:

(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc

Here is the step-by-step breakdown of the formula:

  1. Square each term individually:
    • a^2
    • b^2
    • c^2
  2. Multiply each pair of different terms by 2:
    • 2ab
    • 2ac
    • 2bc
  3. Add all these results together to get the final expanded form:
    • a^2 + b^2 + c^2 + 2ab + 2ac + 2bc
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Using this formula, you can expand any trinomial of the form (a + b + c) squared.

General Terms Table

Here is a table with pre-calculated values for common trinomial terms to help you quickly find the expanded form without calculating each time:

abcExpanded Form
1231 + 4 + 9 + 4 + 6 + 12 = 36
2344 + 9 + 16 + 12 + 16 + 24 = 81
1111 + 1 + 1 + 2 + 2 + 2 = 9
0120 + 1 + 4 + 0 + 0 + 4 = 9
3339 + 9 + 9 + 18 + 18 + 18 = 81

This table provides quick reference values for common trinomials.

Example of Square Trinomial Calculator

Let’s go through an example to illustrate how to use the square trinomial formula.

Calculate (2 + 3 + 4) squared:

  1. Square each term individually:
    • 2 squared = 4
    • 3 squared = 9
    • 4 squared = 16
  2. Multiply each pair of different terms by 2:
    • 2 * 2 * 3 = 12
    • 2 * 2 * 4 = 16
    • 2 * 3 * 4 = 24
  3. Add all these results together:
    • 4 + 9 + 16 + 12 + 16 + 24 = 81
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So, (2 + 3 + 4) squared = 81.

Most Common FAQs

Why is the square trinomial formula important?

The square trinomial formula is important because it simplifies the process of expanding and calculating trinomials, which is essential in algebra and higher-level mathematics.

Can this calculator handle negative numbers?

Yes, the square trinomial calculator can handle negative numbers. Just input the negative values for a, b, and c, and it will provide the correct expanded form.

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