Bewerkingen met veeltermen

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

1. \((5x^2-3)(-4x^2-4)\)
2. \((9x+6)+(9x-10)\)
3. \((2x+5)(3x+6)\)
4. \((-5x^2+14x) +(14x-19) -(+28x+19)\)
5. \((7x^2+18x) +(18x+11) -(+36x-11)\)
6. \((8x^2-6)(-3x^2+5)\)
7. \(-7x(-15x+14y+14)\)
8. \((-x^2+7x)(x-5)\)
9. \((-7x^3+17x^2+14)-(-18x^3+1+2x)-(-19x+x^2+11x^3)\)
10. \(-2x^5(8x^5-4x^2-4)\)
11. \((-5x^2+5)(x^2+8)\)
12. \(19x(-16x^7+9x^2)\)

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

Verbetersleutel

1. \((5x^2-3)(-4x^2-4)\\=-20x^4-20x^2+12x^2+12\\=-20x^4-8x^2+12\)
2. \((9x+6)+(9x-10)\\=9x+6+9x-10\\=18x-4\)
3. \((2x+5)(3x+6)\\=6x^2+12x+15x+30\\=6x^2+27x+30\)
4. \((-5x^2+14x) +(14x-19) -(+28x+19)\\=-5x^2+14x+14x-19-28x-19\\=-5x^2-38\)
5. \((7x^2+18x) +(18x+11) -(+36x-11)\\=7x^2+18x+18x+11-36x+11\\=7x^2+22\)
6. \((8x^2-6)(-3x^2+5)\\=-24x^4+40x^2+18x^2-30\\=-24x^4+58x^2-30\)
7. \(-7x(-15x+14y+14)=105x^2-98xy-98x\)
8. \((-x^2+7x)(x-5)\\=-x^3+5x^2+7x^2-35x\\=-x^3+12x^2-35x\)
9. \((-7x^3+17x^2+14)-(-18x^3+1+2x)-(-19x+x^2+11x^3)\\=-7x^3+17x^2+14+18x^3-1-2x+19x-x^2-11x^3\\=16x^2+17x+13\)
10. \(-2x^5(8x^5-4x^2-4)=-16x^{10}+8x^{7}+8x^5\)
11. \((-5x^2+5)(x^2+8)\\=-5x^4-40x^2+5x^2+40\\=-5x^4-35x^2+40\)
12. \(19x(-16x^7+9x^2)=-304x^8+171x^3\)