Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(x^2-81\)
2. \(81q^{10}-4s^2\)
3. \(9a^{10}-84a^5+196\)
4. \(4q^{6}+20q^3y+25y^2\)
5. \(64s^2-225\)
6. \(b^2+6b+9\)
7. \(25s^{14}-144\)
8. \(q^2+2q+1\)
9. \(q^2+4q+4\)
10. \(49p^{8}-84p^4+36\)
11. \(-9q^2+16\)
12. \(25-64x^{4}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(x^2-81=(x-9)(x+9)\)
2. \(81q^{10}-4s^2=(9q^5+2s)(9q^5-2s)\)
3. \(9a^{10}-84a^5+196=(3a^5-14)^2\)
4. \(4q^{6}+20q^3y+25y^2=(2q^3+5y)^2\)
5. \(64s^2-225=(8s+15)(8s-15)\)
6. \(b^2+6b+9=(b+3)^2\)
7. \(25s^{14}-144=(5s^7+12)(5s^7-12)\)
8. \(q^2+2q+1=(q+1)^2\)
9. \(q^2+4q+4=(q+2)^2\)
10. \(49p^{8}-84p^4+36=(7p^4-6)^2\)
11. \(-9q^2+16=(4-3q)(4+3q)\)
12. \(25-64x^{4}=(5-8x^2)(5+8x^2)\)