Bewerkingen met veeltermen

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

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

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

Verbetersleutel

1. \(-6x(-2x-9y-6)=12x^2+54xy+36x\)
2. \((-10x^3+2x^2+19)-(-3x^3+9+6x)-(-19x+18x^2-12x^3)\\=-10x^3+2x^2+19+3x^3-9-6x+19x-18x^2+12x^3\\=5x^3-16x^2+13x+10\)
3. \(8x^2(-6x^3-6x^2-5)=-48x^{5}-48x^{4}-40x^2\)
4. \((-4x-2)(5x+6)\\=-20x^2-24x-10x-12\\=-20x^2-34x-12\)
5. \(-4x(x^2-5x+5)=-4x^3+20x^2-20x\)
6. \((x^3+19x-6)+(-9x^3+20x^2+5)\\=x^3+19x-6-9x^3+20x^2+5\\=-8x^3+20x^2+19x-1\)
7. \((3x^4-3x^2-5)(2x^2+5)\\=6x^6+15x^4-6x^4-15x^2-10x^2-25\\=6x^6+9x^4-25x^2-25\)
8. \((-3x^3+10x^2+19)-(4x^3+13+16x)-(-18x-x^2-11x^3)\\=-3x^3+10x^2+19-4x^3-13-16x+18x+x^2+11x^3\\=4x^3+11x^2+2x+6\)
9. \((-2x^2-20)-(x^2-13x)\\=-2x^2-20-x^2+13x\\=-3x^2+13x-20\)
10. \(-x^5(6x^4+10x+1)=-6x^9-10x^6-x^5\)
11. \((-x+1)+(-8x-13)\\=-x+1-8x-13\\=-9x-12\)
12. \(2x(-19x+10y-7)=-38x^2+20xy-14x\)