Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(9p^{10}-30p^5x+25x^2\)
2. \(4y^2+28y+49\)
3. \(225y^{4}-420y^2+196\)
4. \(225q^2-49b^{8}\)
5. \(25q^2-49p^{4}\)
6. \(196s^2-308s+121\)
7. \(36s^{6}+84s^3+49\)
8. \(y^2-64\)
9. \(169x^{14}-100\)
10. \(-9y^2+16\)
11. \(256y^{8}-25\)
12. \(-64s^2+9\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(9p^{10}-30p^5x+25x^2=(3p^5-5x)^2\)
2. \(4y^2+28y+49=(2y+7)^2\)
3. \(225y^{4}-420y^2+196=(15y^2-14)^2\)
4. \(225q^2-49b^{8}=(15q-7b^4)(15q+7b^4)\)
5. \(25q^2-49p^{4}=(5q-7p^2)(5q+7p^2)\)
6. \(196s^2-308s+121=(14s-11)^2\)
7. \(36s^{6}+84s^3+49=(6s^3+7)^2\)
8. \(y^2-64=(y-8)(y+8)\)
9. \(169x^{14}-100=(13x^7+10)(13x^7-10)\)
10. \(-9y^2+16=(4-3y)(4+3y)\)
11. \(256y^{8}-25=(16y^4+5)(16y^4-5)\)
12. \(-64s^2+9=(3-8s)(3+8s)\)