Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(s^2-100\)
2. \(49s^{12}-25x^2\)
3. \(100a^{4}+60a^2+9\)
4. \(1-225x^{6}\)
5. \(169y^{6}-156y^3+36\)
6. \(49y^{10}-140y^5+100\)
7. \(36a^2-60a+25\)
8. \(q^2-49\)
9. \(144y^{10}+312y^5+169\)
10. \(q^2+2q+1\)
11. \(9a^{14}-25s^2\)
12. \(256p^{6}+288p^3q+81q^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(s^2-100=(s-10)(s+10)\)
2. \(49s^{12}-25x^2=(7s^6+5x)(7s^6-5x)\)
3. \(100a^{4}+60a^2+9=(10a^2+3)^2\)
4. \(1-225x^{6}=(1-15x^3)(1+15x^3)\)
5. \(169y^{6}-156y^3+36=(13y^3-6)^2\)
6. \(49y^{10}-140y^5+100=(7y^5-10)^2\)
7. \(36a^2-60a+25=(6a-5)^2\)
8. \(q^2-49=(q-7)(q+7)\)
9. \(144y^{10}+312y^5+169=(12y^5+13)^2\)
10. \(q^2+2q+1=(q+1)^2\)
11. \(9a^{14}-25s^2=(3a^7+5s)(3a^7-5s)\)
12. \(256p^{6}+288p^3q+81q^2=(16p^3+9q)^2\)