Direction: Perform the indicated operation.
1. 3m + 5 + m + 1
2. 3b + 3 - b - 1
3. 11b² - b² - 2b²
4. -2n² - 3n³ - n² - 2n³
5. -4x²y³z - (-x²y³z)
Answer (1)
Let's simplify each of the algebraic expressions by performing the indicated operations and combining like terms.
Expression : 3 m + 5 + m + 12
Combine the like terms:
Terms involving m : 3 m + m = 4 m
Constant terms: 5 + 12 = 17
Simplified expression: 4 m + 17
Expression : 3 b + 3 − b − 13
Combine the like terms:
Terms involving b : 3 b − b = 2 b
Constant terms: 3 − 13 = − 10
Simplified expression: 2 b − 10
Expression : 11 b 2 − b 2 − 2 b 2
Combine the like terms (all terms involve b 2 ):
11 b 2 − b 2 − 2 b 2 = ( 11 − 1 − 2 ) b 2 = 8 b 2
Simplified expression: 8 b 2
Expression : − 2 n 2 − 3 n 3 − n 2 − 2 n 3
Combine the like terms:
Terms involving n 3 : − 3 n 3 − 2 n 3 = − 5 n 3
Terms involving n 2 : − 2 n 2 − n 2 = − 3 n 2
Simplified expression: − 5 n 3 − 3 n 2
Expression : − 4 x 2 y 3 z − ( − x 2 y 3 z )
Simplify the expression by removing the parentheses:
− 4 x 2 y 3 z + x 2 y 3 z
Combine the like terms: ( − 4 + 1 ) x 2 y 3 z = − 3 x 2 y 3 z
Simplified expression: − 3 x 2 y 3 z
Each of these expressions has been simplified by combining like terms, ensuring that our answer is as concise as possible.
