Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(q^2+20q+100\)
2. \(81y^{16}-100\)
3. \(b^2-169\)
4. \(16a^{10}-56a^5p+49p^2\)
5. \(36p^{16}-121q^2\)
6. \(q^2-4q+4\)
7. \(25x^{12}-4\)
8. \(p^2-16\)
9. \(169s^{16}-196\)
10. \(100a^{10}-81\)
11. \(-121s^2+196\)
12. \(144a^{10}+24a^5+1\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(q^2+20q+100=(q+10)^2\)
2. \(81y^{16}-100=(9y^8+10)(9y^8-10)\)
3. \(b^2-169=(b+13)(b-13)\)
4. \(16a^{10}-56a^5p+49p^2=(4a^5-7p)^2\)
5. \(36p^{16}-121q^2=(6p^8+11q)(6p^8-11q)\)
6. \(q^2-4q+4=(q-2)^2\)
7. \(25x^{12}-4=(5x^6+2)(5x^6-2)\)
8. \(p^2-16=(p-4)(p+4)\)
9. \(169s^{16}-196=(13s^8+14)(13s^8-14)\)
10. \(100a^{10}-81=(10a^5+9)(10a^5-9)\)
11. \(-121s^2+196=(14-11s)(14+11s)\)
12. \(144a^{10}+24a^5+1=(12a^5+1)^2\)