Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(1-225p^{8}\)
2. \(x^2-18x+81\)
3. \(64a^{10}+240a^5x+225x^2\)
4. \(s^2+20s+100\)
5. \(49y^2-169p^{12}\)
6. \(225s^{10}-4y^2\)
7. \(169p^{4}+182p^2s+49s^2\)
8. \(256q^{10}+224q^5y+49y^2\)
9. \(16a^{8}-121y^2\)
10. \(q^{16}-36x^2\)
11. \(p^2+28p+196\)
12. \(p^2+8p+16\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(1-225p^{8}=(1-15p^4)(1+15p^4)\)
2. \(x^2-18x+81=(x-9)^2\)
3. \(64a^{10}+240a^5x+225x^2=(8a^5+15x)^2\)
4. \(s^2+20s+100=(s+10)^2\)
5. \(49y^2-169p^{12}=(7y-13p^6)(7y+13p^6)\)
6. \(225s^{10}-4y^2=(15s^5+2y)(15s^5-2y)\)
7. \(169p^{4}+182p^2s+49s^2=(13p^2+7s)^2\)
8. \(256q^{10}+224q^5y+49y^2=(16q^5+7y)^2\)
9. \(16a^{8}-121y^2=(4a^4+11y)(4a^4-11y)\)
10. \(q^{16}-36x^2=(q^8+6x)(q^8-6x)\)
11. \(p^2+28p+196=(p+14)^2\)
12. \(p^2+8p+16=(p+4)^2\)