Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(b^2-22b+121\)
2. \(121a^{10}+110a^5p+25p^2\)
3. \(169a^{10}+286a^5+121\)
4. \(9p^{8}+42p^4+49\)
5. \(x^2-16\)
6. \(49p^2-81b^{4}\)
7. \(q^2-9\)
8. \(225a^2-420a+196\)
9. \(16p^2-56p+49\)
10. \(169a^{6}-25p^2\)
11. \(121-49x^{4}\)
12. \(256a^2-96a+9\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(b^2-22b+121=(b-11)^2\)
2. \(121a^{10}+110a^5p+25p^2=(11a^5+5p)^2\)
3. \(169a^{10}+286a^5+121=(13a^5+11)^2\)
4. \(9p^{8}+42p^4+49=(3p^4+7)^2\)
5. \(x^2-16=(x+4)(x-4)\)
6. \(49p^2-81b^{4}=(7p-9b^2)(7p+9b^2)\)
7. \(q^2-9=(q-3)(q+3)\)
8. \(225a^2-420a+196=(15a-14)^2\)
9. \(16p^2-56p+49=(4p-7)^2\)
10. \(169a^{6}-25p^2=(13a^3+5p)(13a^3-5p)\)
11. \(121-49x^{4}=(11-7x^2)(11+7x^2)\)
12. \(256a^2-96a+9=(16a-3)^2\)