Question

спростити вираз:
$( {x}^{2} + 3)( {x}^{2} - 2) - ( {x}^{2} + 4)( {x}^{2} - 1)$
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Answer 1

$\displaystyle\bf\\(x^{2} +3)(x^{2} -2)-(x^{2} +4)(x^{2} -1)=\\\\=x^{2}\cdot x^{2} +x^{2} \cdot (-2)+3\cdot x^{2} +3\cdot (-2)-[x^{2} \cdot x^{2} +x^{2} \cdot (-1)+4\cdot x^{2}+4\cdot(-1)]=\\\\=x^{4} -2x^{2} +3x^{2} -6-x^{4} +x^{2} -4x^{2} +4=\\\\=\underbrace{(x^{4} -x^{4} )}_{0}+\underbrace{(3x^{2} -2x^{2} +x^{2} -4x^{2} )}_{-2x^{2} }+\underbrace{(4-6)}_{-2}=-2x^{2} -2$