Bewerkingen met veeltermen

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

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

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

Verbetersleutel

1. \((2x^3-9x^2-18)-(10x^3-5+10x)-(-12x+10x^2+10x^3)\\=2x^3-9x^2-18-10x^3+5-10x+12x-10x^2-10x^3\\=-18x^3-19x^2+2x-13\)
2. \((6x^2+8)-(-15x^2-7x)\\=6x^2+815x^2+7x\\=21x^2+7x+8\)
3. \(-8x^3(10x^2+5x^5-3)=-40x^{8}-80x^{5}+24x^3\)
4. \(-5x^5(x^5+2x^3-1)=-5x^{10}-10x^{8}+5x^5\)
5. \((10x-17)+(5x-10)\\=10x-17+5x-10\\=15x-27\)
6. \(-8x(-6x^2+7x+5)=48x^3-56x^2-40x\)
7. \((3x^2-4x+3)(3x^{4}+5)\\=9x^{6}+15x^2-12x^{5}-20x+9x^4+15\\=9x^{6}-12x^{5}+9x^4+15x^2-20x+15\)
8. \(x^3(-6x^3+x^4-4)=x^{7}-6x^{6}-4x^3\)
9. \((2x^2-12)-(7x^2-9x)\\=2x^2-12-7x^2+9x\\=-5x^2+9x-12\)
10. \(7x(5x^2-5x-5)=35x^3-35x^2-35x\)
11. \((3x^2-4x+1)(3x^2-4x-3)\\=9x^4-12x^3-9x^2-12x^3+16x^2+12x+3x^2-4x-3\\=9x^4-24x^3+10x^2+8x-3\)
12. \(-x(-x^2-7x+1)=x^3+7x^2-x\)