Bewerkingen met veeltermen

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

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

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

Verbetersleutel

1. \((-2x-1)(-4x-3)\\=8x^2+6x+4x+3\\=8x^2+10x+3\)
2. \(-4x(12x-6y-7)=-48x^2+24xy+28x\)
3. \(-3x^3(6x^6-7x^5+2)=-18x^{9}+21x^{8}-6x^3\)
4. \((-6x-1)(4x+1)\\=-24x^2-6x-4x-1\\=-24x^2-10x-1\)
5. \((-9x^3-18x^2-2)-(-14x^3+16+8x)-(-6x-20x^2+11x^3)\\=-9x^3-18x^2-2+14x^3-16-8x+6x+20x^2-11x^3\\=-6x^3+2x^2-2x-18\)
6. \(-5x(-8x^2-4x-4)=40x^3+20x^2+20x\)
7. \(-4x^5(-4x^6+5x^3+2)=16x^{11}-20x^{8}-8x^5\)
8. \((-x^4-6x^2+1)(2x^2-1)\\=-2x^6+x^4-12x^4+6x^2+2x^2-1\\=-2x^6-11x^4+8x^2-1\)
9. \((-17x^3+x^2+3x)-(-11x^2+2x-10x^3)\\=-17x^3+x^2+3x+11x^2-2x+10x^3\\=-7x^3+12x^2+x\)
10. \((2x^4-4x^2+3)(-3x^2+5)\\=-6x^6+10x^4+12x^4-20x^2-9x^2+15\\=-6x^6+22x^4-29x^2+15\)
11. \(-13x(-8x^8+2x^2)=104x^9-26x^3\)
12. \((4x^2-18)-(19x^2-18x)\\=4x^2-18-19x^2+18x\\=-15x^2+18x-18\)