Add or subtract the following monomials:

1. 4x² + 7x²
2. -5a - 2a
3. 9y - 4y
4. -11xy + 7xy
5. -10ab - 15ab
6. -12c²d² + 8c²d²
7. -10b³c + (-9b³c) + b³c
8. 3x² + 4x + 2x² - 7x - 5

To add or subtract monomials, you need to combine like terms. Like terms are terms that have the same variables raised to the same exponents.
1.) 4 x 2 + 7 x 2 : Both terms have the variable x 2 . Combine them: 4 x 2 + 7 x 2 = ( 4 + 7 ) x 2 = 11 x 2
2.) − 5 a − 2 a : Both terms have the variable a . Combine them: − 5 a − 2 a = ( − 5 − 2 ) a = − 7 a
3.) 9 y − 4 y : Both terms have the variable y . Combine them: 9 y − 4 y = ( 9 − 4 ) y = 5 y
4.) − 11 x y + 7 x y : Both terms have the variable x y . Combine them: − 11 x y + 7 x y = ( − 11 + 7 ) x y = − 4 x y
5.) − 10 ab − 15 ab : Both terms have the variable ab . Combine them: − 10 ab − 15 ab = ( − 10 − 15 ) ab = − 25 ab
6.) − 12 c 2 d 2 + 8 c 2 d 2 : Both terms have the variable c 2 d 2 . Combine them: − 12 c 2 d 2 + 8 c 2 d 2 = ( − 12 + 8 ) c 2 d 2 = − 4 c 2 d 2
7.) − 10 b 3 c + ( − 9 b 3 c ) + b 3 c : All terms have the variable b 3 c . Combine them: − 10 b 3 c + ( − 9 b 3 c ) + b 3 c = ( − 10 − 9 + 1 ) b 3 c = − 18 b 3 c
8.) 3 x 2 + 4 x + 2 x 2 − 7 x − 5 : Identify like terms and combine them:

x 2 terms: 3 x 2 + 2 x 2 = 5 x 2
x terms: 4 x − 7 x = − 3 x
Constant: − 5 Combine all simplified terms: 5 x 2 − 3 x − 5

By understanding and applying the rules for combining like terms in these problems, you can easily add or subtract monomials. Just remember to look for matching variables and matching exponents!

Answered by ElijahBenjaminCarter | 2025-07-07

To add or subtract monomials, combine like terms that share the same variable and exponent. Each problem demonstrates how to simplify expressions by adding or subtracting the coefficients of like terms. The final results are found by applying these rules step by step.
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Answered by ElijahBenjaminCarter | 2025-07-08