Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(9y^{10}+60y^5+100\)
2. \(16p^{10}-120p^5+225\)
3. \(196x^{12}-225\)
4. \(p^2-14p+49\)
5. \(121s^{6}+88s^3+16\)
6. \(225s^{4}-420s^2y+196y^2\)
7. \(100a^{16}-9s^2\)
8. \(256b^{8}-49\)
9. \(225a^2-210a+49\)
10. \(49x^{10}+14x^5+1\)
11. \(25x^{8}-144\)
12. \(169-256p^{16}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(9y^{10}+60y^5+100=(3y^5+10)^2\)
2. \(16p^{10}-120p^5+225=(4p^5-15)^2\)
3. \(196x^{12}-225=(14x^6+15)(14x^6-15)\)
4. \(p^2-14p+49=(p-7)^2\)
5. \(121s^{6}+88s^3+16=(11s^3+4)^2\)
6. \(225s^{4}-420s^2y+196y^2=(15s^2-14y)^2\)
7. \(100a^{16}-9s^2=(10a^8+3s)(10a^8-3s)\)
8. \(256b^{8}-49=(16b^4+7)(16b^4-7)\)
9. \(225a^2-210a+49=(15a-7)^2\)
10. \(49x^{10}+14x^5+1=(7x^5+1)^2\)
11. \(25x^{8}-144=(5x^4+12)(5x^4-12)\)
12. \(169-256p^{16}=(13-16p^8)(13+16p^8)\)