Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25x^{6}+90x^3+81\)
2. \(b^2-64\)
3. \(-144p^2+1\)
4. \(169a^{8}-144\)
5. \(-9p^2+16\)
6. \(-25p^2+196\)
7. \(121q^2-286q+169\)
8. \(81a^{10}-169\)
9. \(256b^{6}-96b^3p+9p^2\)
10. \(100q^2-9\)
11. \(49b^2+14b+1\)
12. \(p^2-16\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25x^{6}+90x^3+81=(5x^3+9)^2\)
2. \(b^2-64=(b-8)(b+8)\)
3. \(-144p^2+1=(1-12p)(1+12p)\)
4. \(169a^{8}-144=(13a^4+12)(13a^4-12)\)
5. \(-9p^2+16=(4-3p)(4+3p)\)
6. \(-25p^2+196=(14-5p)(14+5p)\)
7. \(121q^2-286q+169=(11q-13)^2\)
8. \(81a^{10}-169=(9a^5+13)(9a^5-13)\)
9. \(256b^{6}-96b^3p+9p^2=(16b^3-3p)^2\)
10. \(100q^2-9=(10q+3)(10q-3)\)
11. \(49b^2+14b+1=(7b+1)^2\)
12. \(p^2-16=(p+4)(p-4)\)