Bewerkingen met veeltermen

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

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

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

Verbetersleutel

1. \((16x-7)+(-8x-13)\\=16x-7-8x-13\\=8x-20\)
2. \((-x^2+4x-4)(-x^2-x+3)\\=x^4+x^3-3x^2-4x^3-4x^2+12x+4x^2+4x-12\\=x^4-3x^3-3x^2+16x-12\)
3. \(-4x^4(-10x^5+7x^7+1)=-28x^{11}+40x^{9}-4x^4\)
4. \((-13x^3-8x^2+18x)-(-5x^2-17x+10x^3)\\=-13x^3-8x^2+18x+5x^2+17x-10x^3\\=-23x^3-3x^2+35x\)
5. \((5x-5)(-2x-3)\\=-10x^2-15x+10x+15\\=-10x^2-5x+15\)
6. \(8x(-7x^2+2x-3)=-56x^3+16x^2-24x\)
7. \(-3x^5(10x^2+x^5+1)=-3x^{10}-30x^{7}-3x^5\)
8. \((-5x^3-2x^2+3x)-(-16x^2-5x+15x^3)\\=-5x^3-2x^2+3x+16x^2+5x-15x^3\\=-20x^3+14x^2+8x\)
9. \(13x(-14x^8-x^5)=-182x^9-13x^6\)
10. \((2x^4-5x^2+3)(-x^2-5)\\=-2x^6-10x^4+5x^4+25x^2-3x^2-15\\=-2x^6-5x^4+22x^2-15\)
11. \(4x^4(-3x^6-6x^4-2)=-12x^{10}-24x^{8}-8x^4\)
12. \(-6x^3(-x^3+x^2+1)=6x^{6}-6x^{5}-6x^3\)