Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25p^{10}+10p^5s+1s^2\)
2. \(49p^2-4b^{16}\)
3. \(16-169y^{16}\)
4. \(256a^{6}-288a^3p+81p^2\)
5. \(256y^{14}-1\)
6. \(b^2+10b+25\)
7. \(a^2-30a+225\)
8. \(144a^2+24a+1\)
9. \(25x^{10}-144\)
10. \(100b^{4}+60b^2p+9p^2\)
11. \(-144q^2+25\)
12. \(s^2-20s+100\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25p^{10}+10p^5s+1s^2=(5p^5+s)^2\)
2. \(49p^2-4b^{16}=(7p-2b^8)(7p+2b^8)\)
3. \(16-169y^{16}=(4-13y^8)(4+13y^8)\)
4. \(256a^{6}-288a^3p+81p^2=(16a^3-9p)^2\)
5. \(256y^{14}-1=(16y^7+1)(16y^7-1)\)
6. \(b^2+10b+25=(b+5)^2\)
7. \(a^2-30a+225=(a-15)^2\)
8. \(144a^2+24a+1=(12a+1)^2\)
9. \(25x^{10}-144=(5x^5+12)(5x^5-12)\)
10. \(100b^{4}+60b^2p+9p^2=(10b^2+3p)^2\)
11. \(-144q^2+25=(5-12q)(5+12q)\)
12. \(s^2-20s+100=(s-10)^2\)