Bewerkingen met veeltermen

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Bereken, herleid en rangschik naar dalende macht (ZRM toegestaan)

1. \(6x(-4x^6-17x^3)\)
2. \((-17x^3+17x^2+4)-(-10x^3+13+9x)-(-16x+20x^2-x^3)\)
3. \((-2x^4-x^2+1)(3x^2-3)\)
4. \(6x(6x^2+7x+5)\)
5. \(-6x(5x+7y-14)\)
6. \((3x^2-x+3)(-2x^{6}+4)\)
7. \((2x^2+2x+2)(-2x^2-5x+1)\)
8. \(-6x(-2x^4+6x^3)\)
9. \((x^4-6x^2-3)(-2x^2+3)\)
10. \((13x^3-16x^2-13)-(16x^3+19+15x)-(-18x-5x^2+15x^3)\)
11. \((-18x-10)+(-7x-4)\)
12. \((3x^2-6x)(-3x+7)\)

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Bereken, herleid en rangschik naar dalende macht (ZRM toegestaan)

Verbetersleutel

1. \(6x(-4x^6-17x^3)=-24x^7-102x^4\)
2. \((-17x^3+17x^2+4)-(-10x^3+13+9x)-(-16x+20x^2-x^3)\\=-17x^3+17x^2+4+10x^3-13-9x+16x-20x^2+x^3\\=-6x^3-3x^2+7x-9\)
3. \((-2x^4-x^2+1)(3x^2-3)\\=-6x^6+6x^4-3x^4+3x^2+3x^2-3\\=-6x^6+3x^4+6x^2-3\)
4. \(6x(6x^2+7x+5)=36x^3+42x^2+30x\)
5. \(-6x(5x+7y-14)=-30x^2-42xy+84x\)
6. \((3x^2-x+3)(-2x^{6}+4)\\=-6x^{8}+12x^2+2x^{7}-4x-6x^6+12\\=-6x^{8}+2x^{7}-6x^6+12x^2-4x+12\)
7. \((2x^2+2x+2)(-2x^2-5x+1)\\=-4x^4-10x^3+2x^2-4x^3-10x^2+2x-4x^2-10x+2\\=-4x^4-14x^3-12x^2-8x+2\)
8. \(-6x(-2x^4+6x^3)=12x^5-36x^4\)
9. \((x^4-6x^2-3)(-2x^2+3)\\=-2x^6+3x^4+12x^4-18x^2+6x^2-9\\=-2x^6+15x^4-12x^2-9\)
10. \((13x^3-16x^2-13)-(16x^3+19+15x)-(-18x-5x^2+15x^3)\\=13x^3-16x^2-13-16x^3-19-15x+18x+5x^2-15x^3\\=-18x^3-11x^2+3x-32\)
11. \((-18x-10)+(-7x-4)\\=-18x-10-7x-4\\=-25x-14\)
12. \((3x^2-6x)(-3x+7)\\=-9x^3+21x^2+18x^2-42x\\=-9x^3+39x^2-42x\)