Bewerkingen met veeltermen

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

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

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

Verbetersleutel

1. \((-7x^3+13x^2-16x)-(-3x^2+13x-2x^3)\\=-7x^3+13x^2-16x+3x^2-13x+2x^3\\=-5x^3+16x^2-29x\)
2. \((-8x-5)(5x+2)\\=-40x^2-16x-25x-10\\=-40x^2-41x-10\)
3. \((20x-11)+(-6x-6)\\=20x-11-6x-6\\=14x-17\)
4. \(x(18x-11y+3)=18x^2-11xy+3x\)
5. \(-15x(11x^4+15x^3)=-165x^5-225x^4\)
6. \(-5x^2(10x^2+3x^3+4)=-15x^{5}-50x^{4}-20x^2\)
7. \((11x^3-8x^2+14x)-(-10x^2+17x+19x^3)\\=11x^3-8x^2+14x+10x^2-17x-19x^3\\=-8x^3+2x^2-3x\)
8. \((13x^3-10x^2-3x)-(-5x^2-19x-10x^3)\\=13x^3-10x^2-3x+5x^2+19x+10x^3\\=23x^3-5x^2+16x\)
9. \(6x^3(5x^7-x^4+2)=30x^{10}-6x^{7}+12x^3\)
10. \((19x^2-17)-(20x^2-7x)\\=19x^2-17-20x^2+7x\\=-x^2+7x-17\)
11. \(6x^3(-4x^5-2x^4-3)=-24x^{8}-12x^{7}-18x^3\)
12. \((7x+5)(-4x-4)\\=-28x^2-28x-20x-20\\=-28x^2-48x-20\)