Bewerkingen met veeltermen

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

1. \((3x^2+1)(-x^2+4)\)
2. \((4x^2-3)(-x^2+3)\)
3. \(-6x(-12x+18y-1)\)
4. \((20x^3+3x+20)+(-18x^3+15x^2+13)\)
5. \((-5x^2+16x) +(16x-16) -(+32x+16)\)
6. \(-17x(-4x^4-2x^2)\)
7. \((-10x^2-13x) +(-13x+16) -(-26x-16)\)
8. \(-2x(x^2-8x-1)\)
9. \((-7x^2-2)(-x^2-3)\)
10. \(11x(4x^6+15x^3)\)
11. \(7x(2x^2-4x-5)\)
12. \(x(-8x^2-5x-3)\)

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

Verbetersleutel

1. \((3x^2+1)(-x^2+4)\\=-3x^4+12x^2-x^2+4\\=-3x^4+11x^2+4\)
2. \((4x^2-3)(-x^2+3)\\=-4x^4+12x^2+3x^2-9\\=-4x^4+15x^2-9\)
3. \(-6x(-12x+18y-1)=72x^2-108xy+6x\)
4. \((20x^3+3x+20)+(-18x^3+15x^2+13)\\=20x^3+3x+20-18x^3+15x^2+13\\=2x^3+15x^2+3x+33\)
5. \((-5x^2+16x) +(16x-16) -(+32x+16)\\=-5x^2+16x+16x-16-32x-16\\=-5x^2-32\)
6. \(-17x(-4x^4-2x^2)=68x^5+34x^3\)
7. \((-10x^2-13x) +(-13x+16) -(-26x-16)\\=-10x^2-13x-13x+16+26x+16\\=-10x^2+32\)
8. \(-2x(x^2-8x-1)=-2x^3+16x^2+2x\)
9. \((-7x^2-2)(-x^2-3)\\=7x^4+21x^2+2x^2+6\\=7x^4+23x^2+6\)
10. \(11x(4x^6+15x^3)=44x^7+165x^4\)
11. \(7x(2x^2-4x-5)=14x^3-28x^2-35x\)
12. \(x(-8x^2-5x-3)=-8x^3-5x^2-3x\)