Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25a^{8}-90a^4s+81s^2\)
2. \(169y^2-9b^{4}\)
3. \(81p^{10}+252p^5+196\)
4. \(x^2-16x+64\)
5. \(49y^2-100s^{14}\)
6. \(49a^{16}-225b^2\)
7. \(y^2-144\)
8. \(25p^{8}+10p^4s+1s^2\)
9. \(196a^{4}+308a^2+121\)
10. \(81a^{8}+18a^4+1\)
11. \(x^2-121\)
12. \(100b^{14}-9x^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25a^{8}-90a^4s+81s^2=(5a^4-9s)^2\)
2. \(169y^2-9b^{4}=(13y-3b^2)(13y+3b^2)\)
3. \(81p^{10}+252p^5+196=(9p^5+14)^2\)
4. \(x^2-16x+64=(x-8)^2\)
5. \(49y^2-100s^{14}=(7y-10s^7)(7y+10s^7)\)
6. \(49a^{16}-225b^2=(7a^8+15b)(7a^8-15b)\)
7. \(y^2-144=(y-12)(y+12)\)
8. \(25p^{8}+10p^4s+1s^2=(5p^4+s)^2\)
9. \(196a^{4}+308a^2+121=(14a^2+11)^2\)
10. \(81a^{8}+18a^4+1=(9a^4+1)^2\)
11. \(x^2-121=(x-11)(x+11)\)
12. \(100b^{14}-9x^2=(10b^7+3x)(10b^7-3x)\)