Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(121a^{10}-110a^5s+25s^2\)
2. \(y^2-1\)
3. \(4a^2+28a+49\)
4. \(100-49x^{8}\)
5. \(49s^{12}-25x^2\)
6. \(36s^{10}-25y^2\)
7. \(100y^{8}-180y^4+81\)
8. \(49x^2-140x+100\)
9. \(36a^{4}-60a^2q+25q^2\)
10. \(y^2-169\)
11. \(100y^{10}-9\)
12. \(225b^{14}-16p^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(121a^{10}-110a^5s+25s^2=(11a^5-5s)^2\)
2. \(y^2-1=(y-1)(y+1)\)
3. \(4a^2+28a+49=(2a+7)^2\)
4. \(100-49x^{8}=(10-7x^4)(10+7x^4)\)
5. \(49s^{12}-25x^2=(7s^6+5x)(7s^6-5x)\)
6. \(36s^{10}-25y^2=(6s^5+5y)(6s^5-5y)\)
7. \(100y^{8}-180y^4+81=(10y^4-9)^2\)
8. \(49x^2-140x+100=(7x-10)^2\)
9. \(36a^{4}-60a^2q+25q^2=(6a^2-5q)^2\)
10. \(y^2-169=(y+13)(y-13)\)
11. \(100y^{10}-9=(10y^5+3)(10y^5-3)\)
12. \(225b^{14}-16p^2=(15b^7+4p)(15b^7-4p)\)