Find the sum or difference of the following monomials:

1. 2x + (-5x)
2. -2a² - (-6a²)
3. y + (-y)
4. -9x²y³ - (-9x²y³)
5. 12ab² - ab²
6. -16mn³ + (-12mn³)
7. 10a²b³ - (-8a²b³) + a²b³
8. 7xy + 4xy - (-21xy)
9. -8m²n² + 7m²n² - 15m²n²
10. -b²c³ + (-b²c³) - (-b²c³)

To solve these problems, we need to find the sum or difference of each pair of monomials. We do this by combining like terms, which are terms that have the same variable and the same exponent. Here's how we do it:

2x + (-5x) : 2 x + ( − 5 x ) = 2 x − 5 x = − 3 x

-2a^2 - (-6a^2) : − 2 a 2 − ( − 6 a 2 ) = − 2 a 2 + 6 a 2 = 4 a 2

y + (-y) : y + ( − y ) = y − y = 0

-9x^2y^3 - (-9x^2y^3) : − 9 x 2 y 3 − ( − 9 x 2 y 3 ) = − 9 x 2 y 3 + 9 x 2 y 3 = 0

12ab^2 - ab^2 : 12 a b 2 − a b 2 = 11 a b 2

-16mn^3 + (-12mn^3) : − 16 m n 3 + ( − 12 m n 3 ) = − 16 m n 3 − 12 m n 3 = − 28 m n 3

10a^2b^3 - (-8a^2b^3) + a^2b^3 : 10 a 2 b 3 − ( − 8 a 2 b 3 ) + a 2 b 3 = 10 a 2 b 3 + 8 a 2 b 3 + 1 a 2 b 3 = 19 a 2 b 3

7xy + 4xy - (-21xy) : 7 x y + 4 x y − ( − 21 x y ) = 7 x y + 4 x y + 21 x y = 32 x y

-8m^2n^2 + 7m^2n^2 - 15m^2n^2 : − 8 m 2 n 2 + 7 m 2 n 2 − 15 m 2 n 2 = − 8 m 2 n 2 + 7 m 2 n 2 − 15 m 2 n 2 = − 16 m 2 n 2

-b^2c^3 + (-b^2c^3) - (-b^2c^3) : − b 2 c 3 + ( − b 2 c 3 ) − ( − b 2 c 3 ) = − b 2 c 3 − b 2 c 3 + b 2 c 3 = − b 2 c 3


In each problem, we simply adjusted the negative and positive signs and combined the coefficients of like terms. It's important to pay attention to the signs when adding or subtracting monomials.

Answered by BenjaminOwenLewis | 2025-07-22