Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(196p^{10}+420p^5q+225q^2\)
2. \(196s^{4}+84s^2y+9y^2\)
3. \(b^2-10b+25\)
4. \(225y^{4}+330y^2+121\)
5. \(144q^2-49\)
6. \(225s^{10}-4\)
7. \(144p^{10}+312p^5+169\)
8. \(81b^{6}+36b^3+4\)
9. \(144b^{4}-168b^2x+49x^2\)
10. \(-144p^2+1\)
11. \(p^2+2p+1\)
12. \(169b^{12}-81x^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(196p^{10}+420p^5q+225q^2=(14p^5+15q)^2\)
2. \(196s^{4}+84s^2y+9y^2=(14s^2+3y)^2\)
3. \(b^2-10b+25=(b-5)^2\)
4. \(225y^{4}+330y^2+121=(15y^2+11)^2\)
5. \(144q^2-49=(12q+7)(12q-7)\)
6. \(225s^{10}-4=(15s^5+2)(15s^5-2)\)
7. \(144p^{10}+312p^5+169=(12p^5+13)^2\)
8. \(81b^{6}+36b^3+4=(9b^3+2)^2\)
9. \(144b^{4}-168b^2x+49x^2=(12b^2-7x)^2\)
10. \(-144p^2+1=(1-12p)(1+12p)\)
11. \(p^2+2p+1=(p+1)^2\)
12. \(169b^{12}-81x^2=(13b^6+9x)(13b^6-9x)\)