Subtract the second polynomial from the first:
$(i) x^{4} + x^{2} + x - 1; x^{4} - x^{3} - x^{2} + 1$
$(i i) 5 x^{2} - 2 y + 9; 3 x^{2} + 5 y - 7$

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Solution

$(i) (x^{4} + x^{2} + x - 1) - (x^{4} - x^{3} - x^{2} + 1) = x^{4} + x^{2} + x - 1 - x^{4} + x^{3} + x^{2} - 1$
$= x^{4} - x^{4} + x^{3} + x^{2} + x^{2} + x - 1 - 1 = x^{3} + 2 x^{2} + x - 2$
$(i i) 5 x^{2} - 2 y + 9 - (3 x^{2} + 5 y - 7) = 5 x^{2} - 2 y + 9 - 3 x^{2} - 5 y + 7$
$= 5 x^{2} - 3 x^{2} - 2 y - 5 y + 9 + 7 = 2 x^{2} - 7 y + 16$

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