Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(a^{8}-49q^2\)
2. \(36s^{4}+60s^2x+25x^2\)
3. \(49b^{8}-225\)
4. \(144b^{8}-264b^4y+121y^2\)
5. \(100x^2+220x+121\)
6. \(9a^{8}+6a^4+1\)
7. \(p^2+10p+25\)
8. \(x^2-20x+100\)
9. \(169x^2-36a^{16}\)
10. \(256a^{8}-288a^4b+81b^2\)
11. \(s^2-22s+121\)
12. \(225x^2-121\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(a^{8}-49q^2=(a^4+7q)(a^4-7q)\)
2. \(36s^{4}+60s^2x+25x^2=(6s^2+5x)^2\)
3. \(49b^{8}-225=(7b^4+15)(7b^4-15)\)
4. \(144b^{8}-264b^4y+121y^2=(12b^4-11y)^2\)
5. \(100x^2+220x+121=(10x+11)^2\)
6. \(9a^{8}+6a^4+1=(3a^4+1)^2\)
7. \(p^2+10p+25=(p+5)^2\)
8. \(x^2-20x+100=(x-10)^2\)
9. \(169x^2-36a^{16}=(13x-6a^8)(13x+6a^8)\)
10. \(256a^{8}-288a^4b+81b^2=(16a^4-9b)^2\)
11. \(s^2-22s+121=(s-11)^2\)
12. \(225x^2-121=(15x+11)(15x-11)\)