Bewerkingen met veeltermen

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

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

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

Verbetersleutel

1. \((16x^3-12x+15)+(-14x^3-8x^2+12)\\=16x^3-12x+15-14x^3-8x^2+12\\=2x^3-8x^2-12x+27\)
2. \((20x^3-17x^2+9x)-(-19x^2-3x+2x^3)\\=20x^3-17x^2+9x+19x^2+3x-2x^3\\=18x^3+2x^2+12x\)
3. \((2x^2+4x+1)(-2x^{6}+3)\\=-4x^{8}+6x^2-8x^{7}+12x-2x^6+3\\=-4x^{8}-8x^{7}-2x^6+6x^2+12x+3\)
4. \((12x^3+x^2+10)-(-10x^3-16+20x)-(-20x+12x^2-18x^3)\\=12x^3+x^2+10+10x^3+16-20x+20x-12x^2+18x^3\\=40x^3-11x^2+26\)
5. \((-x+2)(x-5)\\=-x^2+5x+2x-10\\=-x^2+7x-10\)
6. \(7x^5(-4x^7-3x^6+5)=-28x^{12}-21x^{11}+35x^5\)
7. \(-9x(-2x^4-4x^2)=18x^5+36x^3\)
8. \(-3x^4(-x^5-9x^3-2)=3x^{9}+27x^{7}+6x^4\)
9. \((6x^3+10x^2+14x)-(-2x^2-13x+7x^3)\\=6x^3+10x^2+14x+2x^2+13x-7x^3\\=-x^3+12x^2+27x\)
10. \((8x^2+8x)(-x-7)\\=-8x^3-56x^2-8x^2-56x\\=-8x^3-64x^2-56x\)
11. \(20x(18x^6+6x^3)=360x^7+120x^4\)
12. \((-12x^3+3x^2-7x)-(-11x^2+11x-16x^3)\\=-12x^3+3x^2-7x+11x^2-11x+16x^3\\=4x^3+14x^2-18x\)