Add the following expressions:
(i) $x^{3} - 2 x^{2} y + 3 x y^{2} - y^{3}, 2 x^{3} - 5 x y^{2} + 3 x^{2} y - 4 y^{3}$
(ii) $a^{4} - 2 a^{3} b + 3 a b^{3} + 4 a^{2} b^{2} + 3 b^{4}, - 2 a^{4} - 5 a b^{3} + 7 a^{3} b - 6 a^{2} b^{2} + b^{4}$

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Solution

Adding the given expressions, we have
(i) x³- 2x²y + 3xy²- y³+ 2x³- 5xy² + 3x²y- 4y³
Collecting positive and negative like terms together, we get
x³+ 2x³- 2x²y + 3x²y + 3xy²- 5xy²- y³ - 4y³
= 3x³ + x²y - 2xy² - 5y³

(ii) (a⁴- 2a³b + 3ab³ + 4a²b² + 3b⁴) + (-2a⁴- 5ab³ + 7a³b - 6a²b² + b⁴)
a⁴- 2a³b + 3ab³ + 4a²b² + 3b⁴ - 2a⁴- 5ab³ + 7a³b - 6a²b² + b⁴
Collecting positive and negative like terms together, we get
a⁴ - 2a⁴ - 2a³b + 7a³b + 3ab³ - 5ab³ + 4a²b² - 6a²b² + 3b⁴ + b⁴
= - a⁴ + 5a³b - 2ab³ - 2a²b² + 4b⁴

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