Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(64a^{10}+16a^5+1\)
2. \(81x^{16}-1\)
3. \(144s^2-q^{6}\)
4. \(169q^{6}+260q^3s+100s^2\)
5. \(169a^{4}+78a^2y+9y^2\)
6. \(-64a^2+225\)
7. \(16a^{16}-9b^2\)
8. \(4y^2-9a^{12}\)
9. \(100a^{4}-180a^2+81\)
10. \(36x^2-121a^{16}\)
11. \(b^2+2b+1\)
12. \(25y^2-169b^{8}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(64a^{10}+16a^5+1=(8a^5+1)^2\)
2. \(81x^{16}-1=(9x^8+1)(9x^8-1)\)
3. \(144s^2-q^{6}=(12s-q^3)(12s+q^3)\)
4. \(169q^{6}+260q^3s+100s^2=(13q^3+10s)^2\)
5. \(169a^{4}+78a^2y+9y^2=(13a^2+3y)^2\)
6. \(-64a^2+225=(15-8a)(15+8a)\)
7. \(16a^{16}-9b^2=(4a^8+3b)(4a^8-3b)\)
8. \(4y^2-9a^{12}=(2y-3a^6)(2y+3a^6)\)
9. \(100a^{4}-180a^2+81=(10a^2-9)^2\)
10. \(36x^2-121a^{16}=(6x-11a^8)(6x+11a^8)\)
11. \(b^2+2b+1=(b+1)^2\)
12. \(25y^2-169b^{8}=(5y-13b^4)(5y+13b^4)\)