Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(9a^{8}-84a^4q+196q^2\)
2. \(81a^2-1\)
3. \(100q^{10}+220q^5+121\)
4. \(49y^2+112y+64\)
5. \(q^{8}-9x^2\)
6. \(256a^{4}-96a^2q+9q^2\)
7. \(256p^{16}-81\)
8. \(64b^{10}-208b^5x+169x^2\)
9. \(p^2+30p+225\)
10. \(4p^{8}+4p^4q+1q^2\)
11. \(-169x^2+144\)
12. \(144a^2-121\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(9a^{8}-84a^4q+196q^2=(3a^4-14q)^2\)
2. \(81a^2-1=(9a+1)(9a-1)\)
3. \(100q^{10}+220q^5+121=(10q^5+11)^2\)
4. \(49y^2+112y+64=(7y+8)^2\)
5. \(q^{8}-9x^2=(q^4+3x)(q^4-3x)\)
6. \(256a^{4}-96a^2q+9q^2=(16a^2-3q)^2\)
7. \(256p^{16}-81=(16p^8+9)(16p^8-9)\)
8. \(64b^{10}-208b^5x+169x^2=(8b^5-13x)^2\)
9. \(p^2+30p+225=(p+15)^2\)
10. \(4p^{8}+4p^4q+1q^2=(2p^4+q)^2\)
11. \(-169x^2+144=(12-13x)(12+13x)\)
12. \(144a^2-121=(12a+11)(12a-11)\)