Activity 4: find the sum or different of the following monomials. 1. 2×+(-5×)2. -2a²-(-6a²)3. Y+(-y)4. -9x²y²-(-9x²y³)5. 12ab²-ab²6. -16mn³+(-12mn³)7. 10a²b³-(-8a²b³)+a²b³8. 7xy+4xy-(-21xy)9. -8m²n²+7m²n²-15m²n²10. -b²c³+(-b²c³)-(-b²c³11. 15m²n³-12m²n³+8m²n³12. a²b⁴+2a²b⁴-9a²b⁴13. -18xyz+(-5xyz)-(12xyz14. 11ab-6ab-15ab15. -21x⁴+17x⁴-12x⁴​

1. [tex]\bold{2x + (-5x)}[/tex]Write as: [tex]2x - 5x[/tex]Combine coefficients: [tex]2 - 5 = -3[/tex]Result: [tex]\boxed{-3x}[/tex]2. [tex]\bold{-2a^2 - (-6a^2)}[/tex]Minus a negative means plus: [tex]-2a^2 + 6a^2[/tex]Combine coefficients: [tex]-2 + 6 = 4[/tex]Result: [tex]\boxed{4a^2}[/tex]3. [tex]\bold{y + (-y)}[/tex][tex]y - y = 0[/tex]Result: [tex]\boxed{0}[/tex]4. [tex]\bold{-9x^2y^2 - (-9x^2y^3)}[/tex]Minus a negative means plus: [tex]-9x^2y^2 + 9x^2y^3[/tex]These terms differ in the powers of [tex]y[/tex] ([tex]y^2\: vs \: y^3[/tex]) so they cannot be combined.Result: [tex]\boxed{-9x^2y^2 + 9x^2y^3}[/tex]5. [tex]\bold{12ab^2 - ab^2 }[/tex][tex]12ab^2 - 1ab^2 = (12 - 1)ab^2 = 11ab^2[/tex]Result: [tex]\boxed{11ab^2}[/tex]6. [tex]\bold{-16mn^3 + (-12mn^3) }[/tex][tex]-16mn^3 - 12mn^3 = (-16 - 12)mn^3 = -28mn^3[/tex]Result: [tex]\boxed{-28mn^3}[/tex]7. [tex]\bold{10a^2b^3 - (-8a^2b^3) + a^2b^3}[/tex]Minus a negative means plus: [tex]10a^2b^3 + 8a^2b^3 + a^2b^3[/tex]Combine coefficients: [tex]10 + 8 + 1 = 19[/tex]Result: [tex]\boxed{19a^2b^3}[/tex]8. [tex]\bold{7xy + 4xy - (-21xy)}[/tex]Minus a negative means plus: [tex]7xy + 4xy + 21xy[/tex]Combine coefficients: [tex]7 + 4 + 21 = 32[/tex]Result: [tex]\boxed{32xy}[/tex]9. [tex]\bold{-8m^2n^2 + 7m^2n^2 - 15m^2n^2}[/tex]Combine coefficients: [tex]-8 + 7 - 15 = -16[/tex]Result: [tex]\boxed{-16m^2n^2}[/tex]10. [tex]\bold {-b^2c^3 + (-b^2c^3) - (-b^2c^3)}[/tex]Rewrite: [tex]-b^2c^3 - b^2c^3 + b^2c^3[/tex]Combine coefficients: [tex]-1 - 1 + 1 = -1[/tex]Result: [tex]\boxed{-b^2c^3}[/tex]11. [tex]\bold{15m^2n^3 - 12m^2n^3 + 8m^2n^3}[/tex]Combine coefficients: [tex]15 - 12 + 8 = 11[/tex]Result: [tex]\boxed{11m^2n^3}[/tex]12. [tex]\bold{a^2b^4 + 2a^2b^4 - 9a^2b^4}[/tex]Combine coefficients: [tex]1 + 2 - 9 = -6[/tex] Result: [tex]\boxed{-6a^2b^4}[/tex]13. [tex]\bold{-18xyz + (-5xyz) - (12xyz) }[/tex]Rewrite: [tex]-18xyz - 5xyz - 12xyz[/tex]Combine coefficients: [tex]-18 - 5 - 12 = -35[/tex]Result: [tex]\boxed{-35xyz}[/tex] 14. [tex]\bold{11ab - 6ab - 15ab}[/tex]Combine coefficients: [tex]11 - 6 - 15 = -10[/tex]Result: [tex]\boxed{-10ab}[/tex]15. [tex]\bold{-21x^4 + 17x^4 - 12x^4}[/tex] Combine coefficients: [tex]-21 + 17 - 12 = -16[/tex] Result: [tex]\boxed{-16x^4}[/tex]

Answered by Sefton | 2025-07-03