Bewerkingen met veeltermen

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

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

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

Verbetersleutel

1. \((-2x^3-18x-4)+(-11x^3+15x^2+16)\\=-2x^3-18x-4-11x^3+15x^2+16\\=-13x^3+15x^2-18x+12\)
2. \(7x^3(-2x^2+5x^4-3)=35x^{7}-14x^{5}-21x^3\)
3. \((-15x^3-15x^2+7)-(3x^3-6+13x)-(-18x-13x^2+11x^3)\\=-15x^3-15x^2+7-3x^3+6-13x+18x+13x^2-11x^3\\=-29x^3-2x^2+5x+13\)
4. \((-18x^2-10)-(17x^2-13x)\\=-18x^2-10-17x^2+13x\\=-35x^2+13x-10\)
5. \(8x^4(-7x^4+2x+5)=-56x^8+16x^5+40x^4\)
6. \((15x+13)+(-10x-8)\\=15x+13-10x-8\\=5x+5\)
7. \(x^5(-2x^4+4x^5+2)=4x^{10}-2x^{9}+2x^5\)
8. \((12x^3+5x^2+1)-(16x^3-8+15x)-(-20x-9x^2-2x^3)\\=12x^3+5x^2+1-16x^3+8-15x+20x+9x^2+2x^3\\=-2x^3+14x^2+5x+9\)
9. \(-3x^4(10x^2-8x^3-5)=24x^{7}-30x^{6}+15x^4\)
10. \(-4x^3(-x^2-9x-4)=4x^5+36x^4+16x^3\)
11. \((-20x^3-4x^2+4)-(4x^3+4+13x)-(-8x-2x^2+10x^3)\\=-20x^3-4x^2+4-4x^3-4-13x+8x+2x^2-10x^3\\=-34x^3-2x^2-5x\)
12. \((-7x-10)(4x+1)\\=-28x^2-7x-40x-10\\=-28x^2-47x-10\)