Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(81x^2+90x+25\)
2. \(36q^2-1\)
3. \(p^2-2p+1\)
4. \(256p^{8}+288p^4q+81q^2\)
5. \(225p^{6}+210p^3x+49x^2\)
6. \(64s^{10}-49x^2\)
7. \(9q^{6}-12q^3s+4s^2\)
8. \(25q^2+130q+169\)
9. \(100p^{6}-1\)
10. \(81x^{8}-36x^4+4\)
11. \(9x^{8}-4\)
12. \(q^2+18q+81\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(81x^2+90x+25=(9x+5)^2\)
2. \(36q^2-1=(6q+1)(6q-1)\)
3. \(p^2-2p+1=(p-1)^2\)
4. \(256p^{8}+288p^4q+81q^2=(16p^4+9q)^2\)
5. \(225p^{6}+210p^3x+49x^2=(15p^3+7x)^2\)
6. \(64s^{10}-49x^2=(8s^5+7x)(8s^5-7x)\)
7. \(9q^{6}-12q^3s+4s^2=(3q^3-2s)^2\)
8. \(25q^2+130q+169=(5q+13)^2\)
9. \(100p^{6}-1=(10p^3+1)(10p^3-1)\)
10. \(81x^{8}-36x^4+4=(9x^4-2)^2\)
11. \(9x^{8}-4=(3x^4+2)(3x^4-2)\)
12. \(q^2+18q+81=(q+9)^2\)