Find the sum or difference of the following polynomials:

1. 15xy² + 2xy²
2. -4b² - (-b²)
3. (5f² + 2f) - (2f² + f)
4. (8x² + 2x - 9) + (-14x² - 3x - 11)
5. (2x² + 4x - 3) + (-3x² - x + 2)

To find the sum or difference of polynomials, we need to carefully add or subtract the coefficients of like terms. Let's solve each given problem step-by-step:

15xy² + 2xy²
Here, we have like terms, both involving the variable xy².
15 x y 2 + 2 x y 2 = ( 15 + 2 ) x y 2 = 17 x y 2
Thus, the sum is 17 x y 2 .

-4b² - (-b²)
To subtract, we change the sign of the term being subtracted.
− 4 b 2 − ( − b 2 ) = − 4 b 2 + b 2 = − 3 b 2
Therefore, the difference is − 3 b 2 .

(5f² + 2f) - (2f² + f)
Distribute the negative sign and combine like terms:
( 5 f 2 + 2 f ) − ( 2 f 2 + f ) = 5 f 2 + 2 f − 2 f 2 − f = ( 5 f 2 − 2 f 2 ) + ( 2 f − f ) = 3 f 2 + f
The result is 3 f 2 + f .

(8x² + 2x - 9) + (-14x² - 3x - 11)
Add the coefficients of like terms:
( 8 x 2 + 2 x − 9 ) + ( − 14 x 2 − 3 x − 11 ) = ( 8 x 2 − 14 x 2 ) + ( 2 x − 3 x ) + ( − 9 − 11 ) = − 6 x 2 − x − 20
So, the sum is − 6 x 2 − x − 20 .

(2x² + 4x - 3) + (-3x² - x + 2)
Again, add the coefficients of like terms:
( 2 x 2 + 4 x − 3 ) + ( − 3 x 2 − x + 2 ) = ( 2 x 2 − 3 x 2 ) + ( 4 x − x ) + ( − 3 + 2 ) = − x 2 + 3 x − 1
Therefore, the sum is − x 2 + 3 x − 1 .


By carefully combining like terms and applying the rules for addition and subtraction of polynomials, we can easily solve these problems. Make sure to keep track of your signs to avoid mistakes.

Answered by SophiaElizab | 2025-07-06