Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(16a^{16}-25s^2\)
2. \(81s^2-4p^{8}\)
3. \(196-81s^{16}\)
4. \(b^2-14b+49\)
5. \(36a^{10}-60a^5+25\)
6. \(9x^2-64q^{8}\)
7. \(100b^{10}+140b^5q+49q^2\)
8. \(225a^{14}-121q^2\)
9. \(x^2-121\)
10. \(a^2-144\)
11. \(9y^{8}-169\)
12. \(a^2-36\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(16a^{16}-25s^2=(4a^8+5s)(4a^8-5s)\)
2. \(81s^2-4p^{8}=(9s-2p^4)(9s+2p^4)\)
3. \(196-81s^{16}=(14-9s^8)(14+9s^8)\)
4. \(b^2-14b+49=(b-7)^2\)
5. \(36a^{10}-60a^5+25=(6a^5-5)^2\)
6. \(9x^2-64q^{8}=(3x-8q^4)(3x+8q^4)\)
7. \(100b^{10}+140b^5q+49q^2=(10b^5+7q)^2\)
8. \(225a^{14}-121q^2=(15a^7+11q)(15a^7-11q)\)
9. \(x^2-121=(x+11)(x-11)\)
10. \(a^2-144=(a+12)(a-12)\)
11. \(9y^{8}-169=(3y^4+13)(3y^4-13)\)
12. \(a^2-36=(a-6)(a+6)\)