Question

Спростить вираз:
x - (4+3x-x^2) + (2-x^2) =
4 + (-x + 5x^2) - (2x - 3 + x^2) =
5 + (2x^2-x) - (4x^2+5+x) =

Answer 1

$\displaystyle\bf\\1)\\\\x-(4+3x-x^{2} )+(2-x^{2} )=x-4-3x+x^{2} +2-x^{2} =\\\\=\underbrace{(x^{2} -x^{2} )}_{0}+\underbrace{(x-3x)}_{-2x}+\underbrace{(2-4)}_{-2}=-2x-2\\\\2)\\\\4+(-x+5x^{2} )-(2x-3+x^{2} )=4-x+5x^{2} -2x+3-x^{2} =\\\\=\underbrace{(5x^{2} -x^{2} )}_{4x^{2} }-\underbrace{(2x+x)}_{3x}+\underbrace{(4+3)}_{7}=4x^{2} -3x+7\\\\3)\\\\5+(2x^{2} -x)-(4x^{2} +5+x)=5+2x^{2} -x-4x^{2} -5-x=$

$\displaystyle\bf\\=\underbrace{(2x^{2} -4x^{2} )}_{-2x^{2} }-\underbrace{(x+x)}_{2x}+\underbrace{(5-5)}_{0}=-2x^{2} -2x$