Subtracting polynomials might look hard at first, but once you understand it, it’s really simple! Here’s how to do it step by step.

What Are Polynomials?

First, let’s talk about what a polynomial is. A polynomial is a math expression that has variables (like letters) raised to whole number powers. These variables can be added, subtracted, or multiplied together.

For example, $3x^2 + 2x - 5$ is a polynomial.

How to Subtract Polynomials

Here’s a simple guide to help you subtract polynomials.

1. Write Down the Polynomials: Start by clearly writing the two polynomials you want to subtract.

   For example, let’s say you have:

   • $P(x) = 4x^3 + 2x^2 - x + 5$
   • $Q(x) = 2x^3 + 3x^2 + 4$

   You want to calculate $P(x) - Q(x)$.

2. Change the Signs: This part is very important! You need to change all the signs in the polynomial you are taking away.

   So for $Q(x)$, change it to:

   • $- (2x^3 + 3x^2 + 4) = -2x^3 - 3x^2 - 4$.

3. Combine Like Terms: Now, write down $P(x)$ and add the new $-Q(x)$.

   It looks like this:

   $$P(x) - Q(x) = (4x^3 + 2x^2 - x + 5) + (-2x^3 - 3x^2 - 4)$$

   Next, combine the like terms:

   • For the cubes: $4x^3 - 2x^3 = 2x^3$
   • For the squares: $2x^2 - 3x^2 = -1x^2$ (which we can just call $-x^2$)
   • For the linears: $-x$ (nothing to combine with)
   • For the constants: $5 - 4 = 1$

4. Write the Final Result: After combining everything, you will get the final polynomial:

   $$P(x) - Q(x) = 2x^3 - x^2 - x + 1$$

Double-Check Your Work

It’s always a good idea to check your work. You can plug in a number for $x$ into both original polynomials and the answer you got. If the results match, you did it right! This will help you understand how polynomials work.

Some Extra Tips

• Stay Organized: Keep your work neat! Using columns for like terms can help prevent mistakes.
• Practice a Lot: The more you practice subtracting polynomials, the easier it will become. Try different examples until you feel good about it.
• Ask for Help: If you’re struggling, don’t be afraid to ask a friend or teacher for help. Sometimes another explanation makes things clearer.

In the end, subtracting polynomials is all about being clear and organized. With these tips, it should be easy for you! Happy learning!