Răspuns:
Explicație pas cu pas:
a) x³-5x²+2x-7-(x³+4x-1)+(x²+6x+2) = x³-5x²+2x-7-x³-4x+1+x²+6x+2=
= x³-x³-5x²+x²+2x-4x+6x-7+1+2 = -4x²+8x-4 = -4(x²-2x+1) = -4(x-1)²
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b) 3x³-5x²+2x-7-(2x³+2x-1)+(x²+5x+3) = 3x³-5x²+2x-7-2x³-2x+1+x²+5x+3=
= 3x³-2x³-5x²+x²+2x-2x+5x-7+1+3 = x³-4x²+5x-3
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c) (4x³-7x²+6x-2)+(3x²-4x+5)-(x³-4x²+2) =
= 4x³-7x²+6x-2+3x²-4x+5-x³+4x²-2 =
= 4x³-x³-7x²+3x²+4x²+6x-4x-2+5-2 = 3x³+2x+5
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d) 2(x²-4x+1)-3(2x²-5x-3)+4(x-2) = 2x²-8x+2-6x²+15x+9+4x-8 =
= 2x²-6x²-8x+15x+4x+2+9-8 = -4x²+11x+3
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e) 6(x³-5x+2)-3(x³+2x²-1)+4(x²-2x-2) =
= 6x³-30x+12-3x³-6x²+3+4x²-8x-8 =
= 6x³-3x³-6x²+4x²-30x-8x+12+3-8 = 3x³-2x²-38x+7
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f) 4x(x²+2x-3)-3(x³+2x²+5)-2x(x+4) =
= 4x³+8x²-12x-3x³-6x²-15-2x²-8x =
= 4x³-3x³+8x²-6x²-2x²-12x-8x-15 = x³-20x-15
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g) 6x(x²-x-2)-5(x³-4x+2)+3x(2x+3) =
= 6x³-6x²-12x-5x³+20x-10+6x²+9x =
= 6x³-5x³-6x²+6x²-12x+20x+9x-10 = x³+17x-10
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