Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100x^{10}-180x^5+81\)
2. \(225p^2-60p+4\)
3. \(144y^{10}+264y^5+121\)
4. \(256a^{4}-9y^2\)
5. \(225y^{4}-420y^2+196\)
6. \(-169p^2+144\)
7. \(256p^{8}-96p^4+9\)
8. \(81a^{6}-4p^2\)
9. \(256b^{10}-96b^5s+9s^2\)
10. \(49s^2-256b^{14}\)
11. \(-49x^2+169\)
12. \(49-169x^{10}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100x^{10}-180x^5+81=(10x^5-9)^2\)
2. \(225p^2-60p+4=(15p-2)^2\)
3. \(144y^{10}+264y^5+121=(12y^5+11)^2\)
4. \(256a^{4}-9y^2=(16a^2+3y)(16a^2-3y)\)
5. \(225y^{4}-420y^2+196=(15y^2-14)^2\)
6. \(-169p^2+144=(12-13p)(12+13p)\)
7. \(256p^{8}-96p^4+9=(16p^4-3)^2\)
8. \(81a^{6}-4p^2=(9a^3+2p)(9a^3-2p)\)
9. \(256b^{10}-96b^5s+9s^2=(16b^5-3s)^2\)
10. \(49s^2-256b^{14}=(7s-16b^7)(7s+16b^7)\)
11. \(-49x^2+169=(13-7x)(13+7x)\)
12. \(49-169x^{10}=(7-13x^5)(7+13x^5)\)