Bewerkingen met veeltermen

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

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

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

Verbetersleutel

1. \((-7x+3)(4x-4)\\=-28x^2+28x+12x-12\\=-28x^2+40x-12\)
2. \(-3x(7x^2+9x-3)=-21x^3-27x^2+9x\)
3. \((-2x^4+6x^2-4)(x^2-5)\\=-2x^6+10x^4+6x^4-30x^2-4x^2+20\\=-2x^6+16x^4-34x^2+20\)
4. \(5x(-16x^6+19x^4)=-80x^7+95x^5\)
5. \(2x(5x^2-7x-3)=10x^3-14x^2-6x\)
6. \((-4x^3-14x-12)+(-7x^3-2x^2-5)\\=-4x^3-14x-12-7x^3-2x^2-5\\=-11x^3-2x^2-14x-17\)
7. \((-10x-9)+(-13x-3)\\=-10x-9-13x-3\\=-23x-12\)
8. \(19x(-6x^5-13x^3)=-114x^6-247x^4\)
9. \((x^2-4x)(-4x-7)\\=-4x^3-7x^2+16x^2+28x\\=-4x^3+9x^2+28x\)
10. \((11x^3-7x^2-2)-(x^3-12+16x)-(-12x-6x^2-14x^3)\\=11x^3-7x^2-2-x^3+12-16x+12x+6x^2+14x^3\\=24x^3-x^2-4x+10\)
11. \(-3x(-x+18y+11)=3x^2-54xy-33x\)
12. \((-x^2+2x-2)(-2x^2+4x-1)\\=2x^4-4x^3+x^2-4x^3+8x^2-2x+4x^2-8x+2\\=2x^4-8x^3+13x^2-10x+2\)