Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(64p^{4}-240p^2s+225s^2\)
2. \(225b^{12}-121\)
3. \(225a^2-420a+196\)
4. \(25x^{14}-1\)
5. \(9b^{10}-84b^5x+196x^2\)
6. \(169q^2-104q+16\)
7. \(169s^{8}+364s^4y+196y^2\)
8. \(256a^{10}+480a^5s+225s^2\)
9. \(9p^{4}+42p^2x+49x^2\)
10. \(a^2-4a+4\)
11. \(100b^{10}-180b^5+81\)
12. \(p^2-22p+121\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(64p^{4}-240p^2s+225s^2=(8p^2-15s)^2\)
2. \(225b^{12}-121=(15b^6+11)(15b^6-11)\)
3. \(225a^2-420a+196=(15a-14)^2\)
4. \(25x^{14}-1=(5x^7+1)(5x^7-1)\)
5. \(9b^{10}-84b^5x+196x^2=(3b^5-14x)^2\)
6. \(169q^2-104q+16=(13q-4)^2\)
7. \(169s^{8}+364s^4y+196y^2=(13s^4+14y)^2\)
8. \(256a^{10}+480a^5s+225s^2=(16a^5+15s)^2\)
9. \(9p^{4}+42p^2x+49x^2=(3p^2+7x)^2\)
10. \(a^2-4a+4=(a-2)^2\)
11. \(100b^{10}-180b^5+81=(10b^5-9)^2\)
12. \(p^2-22p+121=(p-11)^2\)