Bewerkingen met veeltermen

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

1. \(4x^3(9x^3+8x^7+5)\)
2. \((9x^3+18x+20)+(-6x^3-19x^2+2)\)
3. \((-20x^2-x) +(-x-17) -(-2x+17)\)
4. \(2x(14x^4+14x^2)\)
5. \((-3x^4-2x^2-1)(3x^2+3)\)
6. \((-6x+10)(5x+4)\)
7. \(7x^3(8x^2-x^4+4)\)
8. \((x^2+2x-4)(-3x^{8}+2)\)
9. \((2x^4+2x^2-2)(-3x^2-2)\)
10. \((11x^3-16x^2+20)-(-4x^3+8+15x)-(-3x-x^2+5x^3)\)
11. \((8x^2-14)-(-9x^2-6x)\)
12. \((19x^3+13x+13)+(-8x^3+7x^2-19)\)

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

Verbetersleutel

1. \(4x^3(9x^3+8x^7+5)=32x^{10}+36x^{6}+20x^3\)
2. \((9x^3+18x+20)+(-6x^3-19x^2+2)\\=9x^3+18x+20-6x^3-19x^2+2\\=3x^3-19x^2+18x+22\)
3. \((-20x^2-x) +(-x-17) -(-2x+17)\\=-20x^2-x-x-17+2x-17\\=-20x^2-34\)
4. \(2x(14x^4+14x^2)=28x^5+28x^3\)
5. \((-3x^4-2x^2-1)(3x^2+3)\\=-9x^6-9x^4-6x^4-6x^2-3x^2-3\\=-9x^6-15x^4-9x^2-3\)
6. \((-6x+10)(5x+4)\\=-30x^2-24x+50x+40\\=-30x^2+26x+40\)
7. \(7x^3(8x^2-x^4+4)=-7x^{7}+56x^{5}+28x^3\)
8. \((x^2+2x-4)(-3x^{8}+2)\\=-3x^{10}+2x^2-6x^{9}+4x+12x^8-8\\=-3x^{10}-6x^{9}+12x^8+2x^2+4x-8\)
9. \((2x^4+2x^2-2)(-3x^2-2)\\=-6x^6-4x^4-6x^4-4x^2+6x^2+4\\=-6x^6-10x^4+2x^2+4\)
10. \((11x^3-16x^2+20)-(-4x^3+8+15x)-(-3x-x^2+5x^3)\\=11x^3-16x^2+20+4x^3-8-15x+3x+x^2-5x^3\\=10x^3-15x^2-12x+12\)
11. \((8x^2-14)-(-9x^2-6x)\\=8x^2-149x^2+6x\\=17x^2+6x-14\)
12. \((19x^3+13x+13)+(-8x^3+7x^2-19)\\=19x^3+13x+13-8x^3+7x^2-19\\=11x^3+7x^2+13x-6\)