Bewerkingen met veeltermen

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

1. \((10x^2+14)-(-14x^2-16x)\)
2. \((11x^3-8x^2-19)-(-11x^3+18-8x)-(-9x+18x^2+11x^3)\)
3. \((13x^3-13x^2+4)-(-16x^3-11-18x)-(-13x+13x^2+15x^3)\)
4. \(-8x^4(-4x^3+2x-3)\)
5. \((-15x^2-17x) +(-17x+17) -(-34x-17)\)
6. \((-3x^2-4x+4)(-x^{3}-2)\)
7. \((17x^2+18x) +(18x-2) -(+36x+2)\)
8. \(6x(-7x^2+x+4)\)
9. \((x^4+2x^2-2)(-2x^2-5)\)
10. \(4x(-16x+13y-14)\)
11. \((16x^3+7x^2+2x)-(-9x^2-3x-4x^3)\)
12. \(-2x(-15x^4-16x^3)\)

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

Verbetersleutel

1. \((10x^2+14)-(-14x^2-16x)\\=10x^2+1414x^2+16x\\=24x^2+16x+14\)
2. \((11x^3-8x^2-19)-(-11x^3+18-8x)-(-9x+18x^2+11x^3)\\=11x^3-8x^2-19+11x^3-18+8x+9x-18x^2-11x^3\\=11x^3-26x^2+17x-37\)
3. \((13x^3-13x^2+4)-(-16x^3-11-18x)-(-13x+13x^2+15x^3)\\=13x^3-13x^2+4+16x^3+11+18x+13x-13x^2-15x^3\\=14x^3-26x^2+31x+15\)
4. \(-8x^4(-4x^3+2x-3)=32x^7-16x^5+24x^4\)
5. \((-15x^2-17x) +(-17x+17) -(-34x-17)\\=-15x^2-17x-17x+17+34x+17\\=-15x^2+34\)
6. \((-3x^2-4x+4)(-x^{3}-2)\\=3x^{5}+6x^2+4x^{4}+8x-4x^3-8\\=3x^{5}+4x^{4}-4x^3+6x^2+8x-8\)
7. \((17x^2+18x) +(18x-2) -(+36x+2)\\=17x^2+18x+18x-2-36x-2\\=17x^2-4\)
8. \(6x(-7x^2+x+4)=-42x^3+6x^2+24x\)
9. \((x^4+2x^2-2)(-2x^2-5)\\=-2x^6-5x^4-4x^4-10x^2+4x^2+10\\=-2x^6-9x^4-6x^2+10\)
10. \(4x(-16x+13y-14)=-64x^2+52xy-56x\)
11. \((16x^3+7x^2+2x)-(-9x^2-3x-4x^3)\\=16x^3+7x^2+2x+9x^2+3x+4x^3\\=20x^3+16x^2+5x\)
12. \(-2x(-15x^4-16x^3)=30x^5+32x^4\)