Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(b^2-64\)
2. \(1-225a^{8}\)
3. \(4y^2-9p^{14}\)
4. \(x^2-25\)
5. \(36p^{10}-60p^5s+25s^2\)
6. \(144p^{8}-25y^2\)
7. \(169q^{4}-156q^2+36\)
8. \(s^2+4s+4\)
9. \(169b^{8}+182b^4+49\)
10. \(81q^2-36q+4\)
11. \(-16q^2+1\)
12. \(25a^2-120a+144\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(b^2-64=(b+8)(b-8)\)
2. \(1-225a^{8}=(1-15a^4)(1+15a^4)\)
3. \(4y^2-9p^{14}=(2y-3p^7)(2y+3p^7)\)
4. \(x^2-25=(x+5)(x-5)\)
5. \(36p^{10}-60p^5s+25s^2=(6p^5-5s)^2\)
6. \(144p^{8}-25y^2=(12p^4+5y)(12p^4-5y)\)
7. \(169q^{4}-156q^2+36=(13q^2-6)^2\)
8. \(s^2+4s+4=(s+2)^2\)
9. \(169b^{8}+182b^4+49=(13b^4+7)^2\)
10. \(81q^2-36q+4=(9q-2)^2\)
11. \(-16q^2+1=(1-4q)(1+4q)\)
12. \(25a^2-120a+144=(5a-12)^2\)