Bewerkingen met veeltermen

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

1. \((9x^2-3)-(12x^2-10x)\)
2. \((-17x^3-10x+19)+(-7x^3+8x^2-6)\)
3. \(-5x(-17x+15y-6)\)
4. \(3x^3(-6x^6+3x^5+4)\)
5. \(-18x(-4x^8-4x^2)\)
6. \((20x^3-9x^2-10)-(-13x^3-8+14x)-(-3x+11x^2-6x^3)\)
7. \((-13x^3-4x-15)+(-18x^3-13x^2-9)\)
8. \((5x^2-2x)(5x+4)\)
9. \((x^2-4)(-4x^2-6)\)
10. \(-7x(-4x^6+15x^4)\)
11. \(-8x(-13x-5y-20)\)
12. \((15x^3-6x^2-7)-(10x^3-2+18x)-(-5x-12x^2-13x^3)\)

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

Verbetersleutel

1. \((9x^2-3)-(12x^2-10x)\\=9x^2-3-12x^2+10x\\=-3x^2+10x-3\)
2. \((-17x^3-10x+19)+(-7x^3+8x^2-6)\\=-17x^3-10x+19-7x^3+8x^2-6\\=-24x^3+8x^2-10x+13\)
3. \(-5x(-17x+15y-6)=85x^2-75xy+30x\)
4. \(3x^3(-6x^6+3x^5+4)=-18x^{9}+9x^{8}+12x^3\)
5. \(-18x(-4x^8-4x^2)=72x^9+72x^3\)
6. \((20x^3-9x^2-10)-(-13x^3-8+14x)-(-3x+11x^2-6x^3)\\=20x^3-9x^2-10+13x^3+8-14x+3x-11x^2+6x^3\\=39x^3-20x^2-11x-2\)
7. \((-13x^3-4x-15)+(-18x^3-13x^2-9)\\=-13x^3-4x-15-18x^3-13x^2-9\\=-31x^3-13x^2-4x-24\)
8. \((5x^2-2x)(5x+4)\\=25x^3+20x^2-10x^2-8x\\=25x^3+10x^2-8x\)
9. \((x^2-4)(-4x^2-6)\\=-4x^4-6x^2+16x^2+24\\=-4x^4+10x^2+24\)
10. \(-7x(-4x^6+15x^4)=28x^7-105x^5\)
11. \(-8x(-13x-5y-20)=104x^2+40xy+160x\)
12. \((15x^3-6x^2-7)-(10x^3-2+18x)-(-5x-12x^2-13x^3)\\=15x^3-6x^2-7-10x^3+2-18x+5x+12x^2+13x^3\\=18x^3+6x^2-13x-5\)