1) (-x^4y^2 - 3) + (-14x^4y^2 + 9) 2) (a^2 - 17) - (4a^2 + 8) 3) (-17x^2y + 11xy - 2) + (-11xy - 8) 4) (m^2 - 3m - 5) + (m^2 + 10m - 8)
Answer (1)
Let's simplify each of the given algebraic expressions step-by-step.
Expression : ( − x 4 y 2 − 3 ) + ( − 14 x 4 y 2 + 9 )
To combine the terms, add like terms: − x 4 y 2 − 14 x 4 y 2 = − 15 x 4 y 2 and then, add the constant terms: − 3 + 9 = 6 Thus, the simplified expression is: − 15 x 4 y 2 + 6
Expression : ( a 2 − 17 ) − ( 4 a 2 + 8 )
Distribute the negative sign across the second expression: a 2 − 17 − 4 a 2 − 8 Combine like terms: a 2 − 4 a 2 = − 3 a 2 and the constants: − 17 − 8 = − 25 Thus, the simplified expression is: − 3 a 2 − 25
Expression : ( − 17 x 2 y + 11 x y − 2 ) + ( − 11 x y − 8 )
Combine the terms with x y : 11 x y − 11 x y = 0 Combine the constant terms: − 2 − 8 = − 10 The simplified expression for the rest remains: − 17 x 2 y Therefore, the final simplified expression is: − 17 x 2 y − 10
Expression : ( m 2 − 3 m − 5 ) + ( m 2 + 10 m − 8 )
Combine like terms: m 2 + m 2 = 2 m 2 − 3 m + 10 m = 7 m Combine the constants: − 5 − 8 = − 13 Thus, the simplified expression is: 2 m 2 + 7 m − 13
These solutions simplify each expression by combining like terms, ensuring clarity and correctness at every step.
