91Ó°ÊÓ

Adding polynomials means combining two or more polynomials to form a single polynomial. When you add polynomials, you focus on combining like terms.
Like terms are terms that have the same variable raised to the same power.
For example,

• x^2 terms combine with x^2 terms.
• x terms combine with x terms.
• Constant terms (numbers without variables) combine with other constants.

To add the polynomials, align the like terms and perform the addition on each pair of like terms.
If you have other variables like x, example: \((3x^2 + 4x + 2) + (x^2 + 5x + 3)\),combine the x^2 terms together, the x terms together, and the constant terms together:\( (3x^2 + x^2) + (4x + 5x) + (2 + 3) = 4x^2 + 9x + 5\).

Subtracting polynomials is slightly more complex than adding because you have to distribute the negative sign through the second polynomial first.
This ensures that the sign of each term in the second polynomial is changed before you combine like terms.Let’s break it down:
Suppose you have \( (10r^2 - 20r) - (r - 8)\).First, distribute the negative sign to each term in the second polynomial:\( - (r - 8) = -r + 8 \).Now, rewrite the expression with the distributed terms:\(10r^2 - 20r - r + 8\).Finally, combine the like terms:\(-20r - r= -21r \) resulting in the simplified polynomial:\( 10r^2 - 21r + 8\).
Remember, a common mistake students make is forgetting to distribute the negative sign properly.

Combining like terms is a crucial step in both adding and subtracting polynomials.
Like terms are terms that have the same variables and same exponents.For instance, in the expression \(10r^2 - 21r + 8\), the terms

• \(10r^2\) is a like term
• -21r is another like term.

The constant \(8\) doesn't have a variable so it remains unchanged.

When combining like terms, always focus on aligning terms with the same variables and powers.
Add or subtract the coefficients (the numbers in front of the variables) while keeping the variables unchanged.Returning to our worked problem, when we combined \(-20r\) and -r\(, this became \)-21r$.
This method simplifies the polynomial and makes further operations easier.