Bewerkingen met veeltermen

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

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

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

Verbetersleutel

1. \((10x^2+10)-(-12x^2-6x)\\=10x^2+1012x^2+6x\\=22x^2+6x+10\)
2. \(-7x(-2x-18y-9)=14x^2+126xy+63x\)
3. \(6x(3x^2-8x-4)=18x^3-48x^2-24x\)
4. \(3x(17x-18y+2)=51x^2-54xy+6x\)
5. \((11x^2+3)-(2x^2-17x)\\=11x^2+3-2x^2+17x\\=9x^2+17x+3\)
6. \((-6x^2+10x)(-3x+1)\\=18x^3-6x^2-30x^2+10x\\=18x^3-36x^2+10x\)
7. \((-5x-4)(-5x+8)\\=25x^2-40x+20x-32\\=25x^2-20x-32\)
8. \((-4x-4)(-5x-8)\\=20x^2+32x+20x+32\\=20x^2+52x+32\)
9. \((-19x^3-x+6)+(-16x^3-8x^2-12)\\=-19x^3-x+6-16x^3-8x^2-12\\=-35x^3-8x^2-x-6\)
10. \(2x^4(-5x^4+8x+2)=-10x^8+16x^5+4x^4\)
11. \((7x^2+1)(4x^2-4)\\=28x^4-28x^2+4x^2-4\\=28x^4-24x^2-4\)
12. \((4x^2+10x)(3x-1)\\=12x^3-4x^2+30x^2-10x\\=12x^3+26x^2-10x\)