Bewerkingen met veeltermen

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

1. \(-4x^3(5x^3+8x+1)\)
2. \((-3x^2-x+1)(2x^{7}-4)\)
3. \(-4x(6x^2-3x-2)\)
4. \((-x^4-6x^2-2)(-x^2+3)\)
5. \(-2x^3(-8x^3-6x+4)\)
6. \(-5x(13x+12y+11)\)
7. \((-16x^2-3)-(2x^2-3x)\)
8. \((-5x^3+2x+13)+(-15x^3+14x^2-19)\)
9. \(6x^3(-8x^5-10x^3-1)\)
10. \((x^2+18x) +(18x-3) -(+36x+3)\)
11. \(4x(-18x-13y-2)\)
12. \(-8x^3(2x^2-4x^4+3)\)

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

Verbetersleutel

1. \(-4x^3(5x^3+8x+1)=-20x^6-32x^4-4x^3\)
2. \((-3x^2-x+1)(2x^{7}-4)\\=-6x^{9}+12x^2-2x^{8}+4x+2x^7-4\\=-6x^{9}-2x^{8}+2x^7+12x^2+4x-4\)
3. \(-4x(6x^2-3x-2)=-24x^3+12x^2+8x\)
4. \((-x^4-6x^2-2)(-x^2+3)\\=x^6-3x^4+6x^4-18x^2+2x^2-6\\=x^6+3x^4-16x^2-6\)
5. \(-2x^3(-8x^3-6x+4)=16x^6+12x^4-8x^3\)
6. \(-5x(13x+12y+11)=-65x^2-60xy-55x\)
7. \((-16x^2-3)-(2x^2-3x)\\=-16x^2-3-2x^2+3x\\=-18x^2+3x-3\)
8. \((-5x^3+2x+13)+(-15x^3+14x^2-19)\\=-5x^3+2x+13-15x^3+14x^2-19\\=-20x^3+14x^2+2x-6\)
9. \(6x^3(-8x^5-10x^3-1)=-48x^{8}-60x^{6}-6x^3\)
10. \((x^2+18x) +(18x-3) -(+36x+3)\\=x^2+18x+18x-3-36x-3\\=x^2-6\)
11. \(4x(-18x-13y-2)=-72x^2-52xy-8x\)
12. \(-8x^3(2x^2-4x^4+3)=32x^{7}-16x^{5}-24x^3\)