Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(4a^{10}+4a^5b+1b^2\)
2. \(36x^{8}-121y^2\)
3. \(b^2-144\)
4. \(s^2-14s+49\)
5. \(169s^{8}-52s^4+4\)
6. \(169y^2+286y+121\)
7. \(169y^{8}-312y^4+144\)
8. \(225b^{4}-420b^2s+196s^2\)
9. \(-36s^2+49\)
10. \(s^2-1\)
11. \(100q^{8}-180q^4s+81s^2\)
12. \(-81s^2+49\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(4a^{10}+4a^5b+1b^2=(2a^5+b)^2\)
2. \(36x^{8}-121y^2=(6x^4+11y)(6x^4-11y)\)
3. \(b^2-144=(b-12)(b+12)\)
4. \(s^2-14s+49=(s-7)^2\)
5. \(169s^{8}-52s^4+4=(13s^4-2)^2\)
6. \(169y^2+286y+121=(13y+11)^2\)
7. \(169y^{8}-312y^4+144=(13y^4-12)^2\)
8. \(225b^{4}-420b^2s+196s^2=(15b^2-14s)^2\)
9. \(-36s^2+49=(7-6s)(7+6s)\)
10. \(s^2-1=(s+1)(s-1)\)
11. \(100q^{8}-180q^4s+81s^2=(10q^4-9s)^2\)
12. \(-81s^2+49=(7-9s)(7+9s)\)