Bewerkingen met veeltermen

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

1. \(-4x(14x+2y+17)\)
2. \(-5x^2(-3x^5-2x^4+1)\)
3. \((-20x^2+5)-(-5x^2-2x)\)
4. \(2x(8x^2-8x+2)\)
5. \(-8x^2(5x^2+8x^3-3)\)
6. \((-11x^2-13x) +(-13x-19) -(-26x+19)\)
7. \((-20x-20)+(14x-19)\)
8. \((2x-17)+(2x-4)\)
9. \((19x^3-9x^2+16)-(x^3+12-15x)-(-20x-10x^2-3x^3)\)
10. \((-4x^2-10x)(-5x-8)\)
11. \((-x^2+4x-2)(2x^{3}-3)\)
12. \(-4x^3(-7x^2-7x-5)\)

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

Verbetersleutel

1. \(-4x(14x+2y+17)=-56x^2-8xy-68x\)
2. \(-5x^2(-3x^5-2x^4+1)=15x^{7}+10x^{6}-5x^2\)
3. \((-20x^2+5)-(-5x^2-2x)\\=-20x^2+55x^2+2x\\=-15x^2+2x+5\)
4. \(2x(8x^2-8x+2)=16x^3-16x^2+4x\)
5. \(-8x^2(5x^2+8x^3-3)=-64x^{5}-40x^{4}+24x^2\)
6. \((-11x^2-13x) +(-13x-19) -(-26x+19)\\=-11x^2-13x-13x-19+26x-19\\=-11x^2-38\)
7. \((-20x-20)+(14x-19)\\=-20x-20+14x-19\\=-6x-39\)
8. \((2x-17)+(2x-4)\\=2x-17+2x-4\\=4x-21\)
9. \((19x^3-9x^2+16)-(x^3+12-15x)-(-20x-10x^2-3x^3)\\=19x^3-9x^2+16-x^3-12+15x+20x+10x^2+3x^3\\=21x^3+x^2+35x+4\)
10. \((-4x^2-10x)(-5x-8)\\=20x^3+32x^2+50x^2+80x\\=20x^3+82x^2+80x\)
11. \((-x^2+4x-2)(2x^{3}-3)\\=-2x^{5}+3x^2+8x^{4}-12x-4x^3+6\\=-2x^{5}+8x^{4}-4x^3+3x^2-12x+6\)
12. \(-4x^3(-7x^2-7x-5)=28x^5+28x^4+20x^3\)