Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25s^{4}-120s^2+144\)
2. \(-144b^2+25\)
3. \(25y^2-16x^{10}\)
4. \(81-16p^{8}\)
5. \(q^2-36\)
6. \(196s^{4}+420s^2x+225x^2\)
7. \(225a^2+120a+16\)
8. \(81b^{4}+180b^2x+100x^2\)
9. \(169x^{6}-25\)
10. \(4y^{14}-81\)
11. \(196x^2-364x+169\)
12. \(169s^{8}+104s^4+16\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25s^{4}-120s^2+144=(5s^2-12)^2\)
2. \(-144b^2+25=(5-12b)(5+12b)\)
3. \(25y^2-16x^{10}=(5y-4x^5)(5y+4x^5)\)
4. \(81-16p^{8}=(9-4p^4)(9+4p^4)\)
5. \(q^2-36=(q+6)(q-6)\)
6. \(196s^{4}+420s^2x+225x^2=(14s^2+15x)^2\)
7. \(225a^2+120a+16=(15a+4)^2\)
8. \(81b^{4}+180b^2x+100x^2=(9b^2+10x)^2\)
9. \(169x^{6}-25=(13x^3+5)(13x^3-5)\)
10. \(4y^{14}-81=(2y^7+9)(2y^7-9)\)
11. \(196x^2-364x+169=(14x-13)^2\)
12. \(169s^{8}+104s^4+16=(13s^4+4)^2\)