Bewerkingen met veeltermen

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

1. \((-9x^3-20x^2+11)-(-12x^3+9-18x)-(-6x+19x^2-9x^3)\)
2. \((5x^2+9x) +(9x+18) -(+18x-18)\)
3. \(2x^4(8x^4-5x^2-2)\)
4. \(8x^3(-6x^5-10x^3+1)\)
5. \(18x(19x^4+13x^3)\)
6. \(2x^4(-8x^5-5x^7+3)\)
7. \((-11x^2+13x) +(13x-11) -(+26x+11)\)
8. \((-x^4+6x^2-3)(-2x^2-5)\)
9. \(5x^3(-x^3+5x+1)\)
10. \((-2x^2-4x-1)(3x^{4}-3)\)
11. \((3x^2-2x+4)(-3x^2+5x+3)\)
12. \(3x(11x-17y+16)\)

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

Verbetersleutel

1. \((-9x^3-20x^2+11)-(-12x^3+9-18x)-(-6x+19x^2-9x^3)\\=-9x^3-20x^2+11+12x^3-9+18x+6x-19x^2+9x^3\\=12x^3-39x^2+24x+2\)
2. \((5x^2+9x) +(9x+18) -(+18x-18)\\=5x^2+9x+9x+18-18x+18\\=5x^2+36\)
3. \(2x^4(8x^4-5x^2-2)=16x^{8}-10x^{6}-4x^4\)
4. \(8x^3(-6x^5-10x^3+1)=-48x^{8}-80x^{6}+8x^3\)
5. \(18x(19x^4+13x^3)=342x^5+234x^4\)
6. \(2x^4(-8x^5-5x^7+3)=-10x^{11}-16x^{9}+6x^4\)
7. \((-11x^2+13x) +(13x-11) -(+26x+11)\\=-11x^2+13x+13x-11-26x-11\\=-11x^2-22\)
8. \((-x^4+6x^2-3)(-2x^2-5)\\=2x^6+5x^4-12x^4-30x^2+6x^2+15\\=2x^6-7x^4-24x^2+15\)
9. \(5x^3(-x^3+5x+1)=-5x^6+25x^4+5x^3\)
10. \((-2x^2-4x-1)(3x^{4}-3)\\=-6x^{6}+6x^2-12x^{5}+12x-3x^4+3\\=-6x^{6}-12x^{5}-3x^4+6x^2+12x+3\)
11. \((3x^2-2x+4)(-3x^2+5x+3)\\=-9x^4+15x^3+9x^2+6x^3-10x^2-6x-12x^2+20x+12\\=-9x^4+21x^3-13x^2+14x+12\)
12. \(3x(11x-17y+16)=33x^2-51xy+48x\)