Find the sum or difference of the following monomials:
1. 2x + (-5x)
2. -2a^2 - (-6a^2)
3. y + (-y)
4. -9x^2y^3 - (-9x^2y^3)
5. -16mn^3 + (-12mn^3)
6. 10a^2b^3 - (-8a^2b^3)
7. -21x^4 + 17x^4 - 12x^4
8. 18xyz + (-5xyz) - (-12xyz)
Answer (2)
To find the sum or difference of monomials, we combine like terms. Like terms have the same variable and exponents.
2 x + ( − 5 x )
Combine like terms: 2 x − 5 x = − 3 x .
− 2 a 2 − ( − 6 a 2 )
Simplify by subtracting a negative: − 2 a 2 + 6 a 2 = 4 a 2 .
y + ( − y )
Combine like terms: y − y = 0 .
− 9 x 2 y 3 − ( − 9 x 2 y 3 )
Simplify by subtracting a negative: − 9 x 2 y 3 + 9 x 2 y 3 = 0 .
− 16 m n 3 + ( − 12 m n 3 )
Combine like terms: − 16 m n 3 − 12 m n 3 = − 28 m n 3 .
10 a 2 b 3 − ( − 8 a 3 ) h a 3 b
Without any specific instructions, this expression can't be simplified further due to different exponents and variables.
− 21 x 4 + 17 x 4 − 12 x 4
Combine like terms: − 21 x 4 + 17 x 4 − 12 x 4 = − 16 x 4 .
18 x yz + ( − 5 x yz ) − ( − 12 x yz )
Simplify by subtracting a negative: 18 x yz − 5 x yz + 12 x yz = 25 x yz .
By understanding how to recognize and combine like terms, you can simplify expressions with monomials efficiently.
To combine the given monomials, we added or subtracted like terms. The final results for each expression are: -3x, 4a², 0, 0, -28mn³, 18a²b³, -16x⁴, and 25xyz. Understanding how to simplify monomials is key in algebra.
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