Bewerkingen met veeltermen

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

1. \((-10x^2+2)-(-13x^2-7x)\)
2. \((15x+2)+(6x-15)\)
3. \(8x(-3x-9y-7)\)
4. \((-6x-9)(-2x-2)\)
5. \((x^2+4x+3)(-3x^{3}-3)\)
6. \((3x^3-4x^2+13x)-(-18x^2-14x+18x^3)\)
7. \((-19x^2+2x) +(2x-8) -(+4x+8)\)
8. \(-3x^2(-3x^3-7x-2)\)
9. \(-2x(5x^5+17x^4)\)
10. \((2x^4+4x^2+3)(2x^2+4)\)
11. \((2x^2-4x-3)(-3x^2+5x-3)\)
12. \((6x-2)(-2x+1)\)

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

Verbetersleutel

1. \((-10x^2+2)-(-13x^2-7x)\\=-10x^2+213x^2+7x\\=3x^2+7x+2\)
2. \((15x+2)+(6x-15)\\=15x+2+6x-15\\=21x-13\)
3. \(8x(-3x-9y-7)=-24x^2-72xy-56x\)
4. \((-6x-9)(-2x-2)\\=12x^2+12x+18x+18\\=12x^2+30x+18\)
5. \((x^2+4x+3)(-3x^{3}-3)\\=-3x^{5}-3x^2-12x^{4}-12x-9x^3-9\\=-3x^{5}-12x^{4}-9x^3-3x^2-12x-9\)
6. \((3x^3-4x^2+13x)-(-18x^2-14x+18x^3)\\=3x^3-4x^2+13x+18x^2+14x-18x^3\\=-15x^3+14x^2+27x\)
7. \((-19x^2+2x) +(2x-8) -(+4x+8)\\=-19x^2+2x+2x-8-4x-8\\=-19x^2-16\)
8. \(-3x^2(-3x^3-7x-2)=9x^5+21x^3+6x^2\)
9. \(-2x(5x^5+17x^4)=-10x^6-34x^5\)
10. \((2x^4+4x^2+3)(2x^2+4)\\=4x^6+8x^4+8x^4+16x^2+6x^2+12\\=4x^6+16x^4+22x^2+12\)
11. \((2x^2-4x-3)(-3x^2+5x-3)\\=-6x^4+10x^3-6x^2+12x^3-20x^2+12x+9x^2-15x+9\\=-6x^4+22x^3-17x^2-3x+9\)
12. \((6x-2)(-2x+1)\\=-12x^2+6x+4x-2\\=-12x^2+10x-2\)