Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(p^2-81\)
2. \(16a^{8}+24a^4+9\)
3. \(p^2-6p+9\)
4. \(9q^{4}-84q^2+196\)
5. \(81a^{10}+18a^5+1\)
6. \(81s^{8}-198s^4+121\)
7. \(p^2+2p+1\)
8. \(100y^2-260y+169\)
9. \(4-169b^{4}\)
10. \(-121y^2+100\)
11. \(a^2-49\)
12. \(49b^{8}+56b^4x+16x^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(p^2-81=(p+9)(p-9)\)
2. \(16a^{8}+24a^4+9=(4a^4+3)^2\)
3. \(p^2-6p+9=(p-3)^2\)
4. \(9q^{4}-84q^2+196=(3q^2-14)^2\)
5. \(81a^{10}+18a^5+1=(9a^5+1)^2\)
6. \(81s^{8}-198s^4+121=(9s^4-11)^2\)
7. \(p^2+2p+1=(p+1)^2\)
8. \(100y^2-260y+169=(10y-13)^2\)
9. \(4-169b^{4}=(2-13b^2)(2+13b^2)\)
10. \(-121y^2+100=(10-11y)(10+11y)\)
11. \(a^2-49=(a-7)(a+7)\)
12. \(49b^{8}+56b^4x+16x^2=(7b^4+4x)^2\)