Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(121a^{8}-44a^4q+4q^2\)
2. \(x^2-30x+225\)
3. \(-256q^2+49\)
4. \(121p^{8}-176p^4+64\)
5. \(s^2-64\)
6. \(100p^{10}-260p^5+169\)
7. \(100y^{4}+140y^2+49\)
8. \(121q^{8}-220q^4x+100x^2\)
9. \(225q^{8}-420q^4y+196y^2\)
10. \(y^2-225\)
11. \(225x^2-49\)
12. \(1-36a^{10}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(121a^{8}-44a^4q+4q^2=(11a^4-2q)^2\)
2. \(x^2-30x+225=(x-15)^2\)
3. \(-256q^2+49=(7-16q)(7+16q)\)
4. \(121p^{8}-176p^4+64=(11p^4-8)^2\)
5. \(s^2-64=(s+8)(s-8)\)
6. \(100p^{10}-260p^5+169=(10p^5-13)^2\)
7. \(100y^{4}+140y^2+49=(10y^2+7)^2\)
8. \(121q^{8}-220q^4x+100x^2=(11q^4-10x)^2\)
9. \(225q^{8}-420q^4y+196y^2=(15q^4-14y)^2\)
10. \(y^2-225=(y+15)(y-15)\)
11. \(225x^2-49=(15x+7)(15x-7)\)
12. \(1-36a^{10}=(1-6a^5)(1+6a^5)\)