$(x^{5} + 1), (3 - x^{4}), (4 + x^{3} + x^{6})$ $-$
$(2 a^{3} - 3 b^{5}), (2 a^{3} + 3 b^{5}), (2 a^{4} - 3 a^{2} b^{2} + b^{4})$

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Solution

Solution :- Given $(x^{5} + 1), (3 - x^{4}), (4 + x^{3} + x^{6}),$
$(2 a^{3} - 3 b^{5}), (2 a^{3} + 3 b^{5}), (2 a^{4} - 3 a^{2} b^{2} + b^{4})$
Let subtract and add the terms
$\Rightarrow x^{5} + 1 + 3 - x^{4} + 4 + x^{3} + x^{6} + 2 a^{3} - 3 b^{5} + 2 a^{3} + 3 b^{5}$
$+ 2 a^{4} - 3 a^{2} b^{2} + b^{4}$
$\Rightarrow x^{6} + x^{5} - x^{4} + x^{3} + 8 + 4 a^{3} + 2 a^{4} - 3 a^{2} b^{2} + b^{4}$

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(x5+1),(3−x4),(4+x3+x6) −(2a3−3b5),(2a3+3b5),(2a4−3a2b2+b4)

Solution :- Given (x5+1),(3−x4),(4+x3+x6),(2a3−3b5),(2a3+3b5),(2a4−3a2b2+b4)Let subtract and add the terms⇒x5+1+3−x4+4+x3+x6+2a3−3b5+2a3+3b5 +2a4−3a2b2+b4⇒x6+x5−x4+x3+8+4a3+2a4−3a2b2+b4

$(x^{5} + 1), (3 - x^{4}), (4 + x^{3} + x^{6})$ $-$
$(2 a^{3} - 3 b^{5}), (2 a^{3} + 3 b^{5}), (2 a^{4} - 3 a^{2} b^{2} + b^{4})$