Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(81-256y^{10}\)
2. \(25x^{10}-36\)
3. \(49s^{4}+28s^2+4\)
4. \(-16b^2+1\)
5. \(100y^2-b^{6}\)
6. \(a^2-36\)
7. \(144b^{4}+24b^2p+1p^2\)
8. \(64y^{4}+112y^2+49\)
9. \(256a^{8}+288a^4s+81s^2\)
10. \(16s^{6}+120s^3+225\)
11. \(225a^{8}+390a^4x+169x^2\)
12. \(q^2-9\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(81-256y^{10}=(9-16y^5)(9+16y^5)\)
2. \(25x^{10}-36=(5x^5+6)(5x^5-6)\)
3. \(49s^{4}+28s^2+4=(7s^2+2)^2\)
4. \(-16b^2+1=(1-4b)(1+4b)\)
5. \(100y^2-b^{6}=(10y-b^3)(10y+b^3)\)
6. \(a^2-36=(a-6)(a+6)\)
7. \(144b^{4}+24b^2p+1p^2=(12b^2+p)^2\)
8. \(64y^{4}+112y^2+49=(8y^2+7)^2\)
9. \(256a^{8}+288a^4s+81s^2=(16a^4+9s)^2\)
10. \(16s^{6}+120s^3+225=(4s^3+15)^2\)
11. \(225a^{8}+390a^4x+169x^2=(15a^4+13x)^2\)
12. \(q^2-9=(q-3)(q+3)\)