Adding and Subtracting Polynomials

Calculator for Adding and Subtracting Polynomials

How to Use the Adding and Subtracting Polynomials Calculator

The following steps will guide you on how to use the Wolfram Alpha calculator widget for adding and subtracting polynomials. This widget allows you to input polynomial expressions and perform operations like addition, subtraction, and more.

Step 1: Access the Widget

Ensure that the calculator widget is visible on the page. If not, refresh the page to load the script correctly. The widget can be found embedded below:

Step 2: Enter the First Polynomial Expression

In the first input box labeled “First Polynomial,” type in the polynomial expression you want to add or subtract. For example, you could enter \( 3x^2 + 2x – 5 \).

Step 3: Enter the Second Polynomial Expression

In the second input box labeled “Second Polynomial,” enter the second polynomial expression. For instance, input \( x^2 – 3x + 4 \). Make sure that both polynomials are written in standard algebraic format using variables, coefficients, and exponents.

Step 4: Select the Operation (Addition or Subtraction)

After entering the two polynomial expressions, choose whether you want to add or subtract them. Look for the dropdown or radio buttons within the widget to select the desired operation. For example, select “Addition” to add the polynomials \( (3x^2 + 2x – 5) + (x^2 – 3x + 4) \).

Step 5: Click the “Calculate” Button

Once you have entered both polynomials and selected the desired operation (addition or subtraction), click the “Calculate” button on the widget. The calculator will process your input and display the result below the input fields.

Step 6: View the Result

The result of the operation will be displayed beneath the widget. For example, if you are adding \( (3x^2 + 2x – 5) + (x^2 – 3x + 4) \), the result will be \( 4x^2 – x – 1 \).

Step 7: Perform More Calculations (Optional)

If you want to perform more operations on different polynomials, simply clear the input fields and enter new polynomial expressions. You can repeat the process as many times as needed for additional calculations.

Polynomials are algebraic expressions that consist of terms made up of variables and coefficients. When adding or subtracting polynomials, the key is to combine the like terms, which are terms that have the same variable raised to the same power. In this tutorial, we’ll explore how to add and subtract polynomials through four detailed examples.

Steps for Adding Polynomials

Step 1: Arrange the polynomials in standard form (if needed), with like terms aligned vertically or next to each other.
Step 2: Identify and combine the like terms by adding their coefficients while keeping the variable and exponent unchanged.
Step 3: Simplify the expression.

Steps for Subtracting Polynomials

Step 1: Distribute the negative sign to all the terms of the polynomial being subtracted.
Step 2: Combine the like terms by subtracting their coefficients while keeping the variable and exponent unchanged.
Step 3: Simplify the expression.

Example 1: Adding Two Polynomials

Add \( (2x^2 + 3x + 4) \) and \( (x^2 + 5x + 6) \).

Step 1: Align the polynomials based on their degrees:
\[
(2x^2 + 3x + 4) + (x^2 + 5x + 6)
\]
Step 2: Add the coefficients of the like terms:
\[
(2x^2 + x^2) + (3x + 5x) + (4 + 6)
\]
Step 3: Simplify:
\[
3x^2 + 8x + 10
\]

Example 2: Subtracting Two Polynomials

Subtract \( (3x^2 + 4x – 5) \) from \( (5x^2 – 2x + 7) \).

Step 1: Write the subtraction problem:
\[
(5x^2 – 2x + 7) – (3x^2 + 4x – 5)
\]
Step 2: Distribute the negative sign:
\[
5x^2 – 2x + 7 – 3x^2 – 4x + 5
\]
Step 3: Combine the like terms:
\[
(5x^2 – 3x^2) + (-2x – 4x) + (7 + 5)
\]
Step 4: Simplify:
\[
2x^2 – 6x + 12
\]

Example 3: Adding Polynomials with Different Numbers of Terms

Add \( (4x^3 + 2x^2 – 3x) \) and \( (x^2 + 5) \).

Step 1: Align the polynomials:
\[
(4x^3 + 2x^2 – 3x + 0) + (0x^3 + x^2 + 0x + 5)
\]
Step 2: Add the like terms:
\[
(4x^3 + 0x^3) + (2x^2 + x^2) + (-3x + 0x) + (0 + 5)
\]
Step 3: Simplify:
\[
4x^3 + 3x^2 – 3x + 5
\]

Example 4: Subtracting Polynomials with Multiple Variables

Subtract \( (6x^2y + 4xy – 3y^2) \) from \( (8x^2y – xy + 2y^2) \).

Step 1: Write the subtraction problem:
\[
(8x^2y – xy + 2y^2) – (6x^2y + 4xy – 3y^2)
\]
Step 2: Distribute the negative sign:
\[
8x^2y – xy + 2y^2 – 6x^2y – 4xy + 3y^2
\]
Step 3: Combine the like terms:
\[
(8x^2y – 6x^2y) + (-xy – 4xy) + (2y^2 + 3y^2)
\]
Step 4: Simplify:
\[
2x^2y – 5xy + 5y^2
\]

Conclusion

Adding and subtracting polynomials is a straightforward process once you understand how to combine like terms. By following the steps outlined in the examples above, you can easily solve polynomial addition and subtraction problems, even when working with multiple variables or different numbers of terms.

TutorialKart

Adding and Subtracting Polynomials – Calculator, Examples