Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(4q^2+12q+9\)
2. \(9s^{10}+6s^5x+1x^2\)
3. \(9y^2-12y+4\)
4. \(225-16x^{10}\)
5. \(p^{10}-121y^2\)
6. \(y^2-10y+25\)
7. \(16b^{6}-169\)
8. \(169b^{6}-390b^3x+225x^2\)
9. \(196b^2+28b+1\)
10. \(121q^{4}-176q^2+64\)
11. \(49b^{8}-140b^4+100\)
12. \(81-196q^{8}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(4q^2+12q+9=(2q+3)^2\)
2. \(9s^{10}+6s^5x+1x^2=(3s^5+x)^2\)
3. \(9y^2-12y+4=(3y-2)^2\)
4. \(225-16x^{10}=(15-4x^5)(15+4x^5)\)
5. \(p^{10}-121y^2=(p^5+11y)(p^5-11y)\)
6. \(y^2-10y+25=(y-5)^2\)
7. \(16b^{6}-169=(4b^3+13)(4b^3-13)\)
8. \(169b^{6}-390b^3x+225x^2=(13b^3-15x)^2\)
9. \(196b^2+28b+1=(14b+1)^2\)
10. \(121q^{4}-176q^2+64=(11q^2-8)^2\)
11. \(49b^{8}-140b^4+100=(7b^4-10)^2\)
12. \(81-196q^{8}=(9-14q^4)(9+14q^4)\)