Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100s^{8}-121\)
2. \(y^2-2y+1\)
3. \(q^2-1\)
4. \(256a^{4}-288a^2s+81s^2\)
5. \(121y^2+44y+4\)
6. \(225a^{16}-49y^2\)
7. \(144p^2+120p+25\)
8. \(4a^{10}+4a^5+1\)
9. \(-256a^2+25\)
10. \(81b^{8}+72b^4+16\)
11. \(-100s^2+81\)
12. \(b^2-22b+121\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100s^{8}-121=(10s^4+11)(10s^4-11)\)
2. \(y^2-2y+1=(y-1)^2\)
3. \(q^2-1=(q+1)(q-1)\)
4. \(256a^{4}-288a^2s+81s^2=(16a^2-9s)^2\)
5. \(121y^2+44y+4=(11y+2)^2\)
6. \(225a^{16}-49y^2=(15a^8+7y)(15a^8-7y)\)
7. \(144p^2+120p+25=(12p+5)^2\)
8. \(4a^{10}+4a^5+1=(2a^5+1)^2\)
9. \(-256a^2+25=(5-16a)(5+16a)\)
10. \(81b^{8}+72b^4+16=(9b^4+4)^2\)
11. \(-100s^2+81=(9-10s)(9+10s)\)
12. \(b^2-22b+121=(b-11)^2\)