Bewerkingen met veeltermen

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

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

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

Verbetersleutel

1. \(-4x^4(7x^3+2x^4-5)=-8x^{8}-28x^{7}+20x^4\)
2. \(2x^2(-8x^2+x^6+3)=2x^{8}-16x^{4}+6x^2\)
3. \((-8x+4)(3x+7)\\=-24x^2-56x+12x+28\\=-24x^2-44x+28\)
4. \(17x(15x^4-10x^3)=255x^5-170x^4\)
5. \(-4x^2(-x^3+9x-5)=4x^5-36x^3+20x^2\)
6. \((-6x^3-12x^2+14)-(-10x^3+6-16x)-(-10x+8x^2+17x^3)\\=-6x^3-12x^2+14+10x^3-6+16x+10x-8x^2-17x^3\\=-13x^3-20x^2+26x+8\)
7. \((2x^2+8)-(4x^2-16x)\\=2x^2+8-4x^2+16x\\=-2x^2+16x+8\)
8. \((15x^2+18x) +(18x+15) -(+36x-15)\\=15x^2+18x+18x+15-36x+15\\=15x^2+30\)
9. \(-7x(-4x^2+8x+2)=28x^3-56x^2-14x\)
10. \((6x^2-4x)(-4x+4)\\=-24x^3+24x^2+16x^2-16x\\=-24x^3+40x^2-16x\)
11. \(2x^3(-x^5-3x^3-3)=-2x^{8}-6x^{6}-6x^3\)
12. \(-6x^2(4x^3+2x+1)=-24x^5-12x^3-6x^2\)