Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(16-225p^{4}\)
2. \(4x^{10}+12x^5y+9y^2\)
3. \(144a^{6}+120a^3s+25s^2\)
4. \(16a^{12}-81p^2\)
5. \(225p^{4}-60p^2q+4q^2\)
6. \(a^2-16\)
7. \(64y^2-225q^{12}\)
8. \(49q^{6}-182q^3s+169s^2\)
9. \(q^2-196\)
10. \(16p^2-49a^{10}\)
11. \(100x^{6}-60x^3+9\)
12. \(-81p^2+100\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(16-225p^{4}=(4-15p^2)(4+15p^2)\)
2. \(4x^{10}+12x^5y+9y^2=(2x^5+3y)^2\)
3. \(144a^{6}+120a^3s+25s^2=(12a^3+5s)^2\)
4. \(16a^{12}-81p^2=(4a^6+9p)(4a^6-9p)\)
5. \(225p^{4}-60p^2q+4q^2=(15p^2-2q)^2\)
6. \(a^2-16=(a+4)(a-4)\)
7. \(64y^2-225q^{12}=(8y-15q^6)(8y+15q^6)\)
8. \(49q^{6}-182q^3s+169s^2=(7q^3-13s)^2\)
9. \(q^2-196=(q+14)(q-14)\)
10. \(16p^2-49a^{10}=(4p-7a^5)(4p+7a^5)\)
11. \(100x^{6}-60x^3+9=(10x^3-3)^2\)
12. \(-81p^2+100=(10-9p)(10+9p)\)