Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(121a^{10}-286a^5b+169b^2\)
2. \(4x^{4}+4x^2+1\)
3. \(36s^2-49\)
4. \(49b^{4}+140b^2y+100y^2\)
5. \(49-36a^{6}\)
6. \(9a^{10}-48a^5b+64b^2\)
7. \(b^2-25\)
8. \(169p^{4}+130p^2x+25x^2\)
9. \(x^2-169\)
10. \(4x^{14}-169\)
11. \(q^2-12q+36\)
12. \(9-256p^{10}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(121a^{10}-286a^5b+169b^2=(11a^5-13b)^2\)
2. \(4x^{4}+4x^2+1=(2x^2+1)^2\)
3. \(36s^2-49=(6s+7)(6s-7)\)
4. \(49b^{4}+140b^2y+100y^2=(7b^2+10y)^2\)
5. \(49-36a^{6}=(7-6a^3)(7+6a^3)\)
6. \(9a^{10}-48a^5b+64b^2=(3a^5-8b)^2\)
7. \(b^2-25=(b+5)(b-5)\)
8. \(169p^{4}+130p^2x+25x^2=(13p^2+5x)^2\)
9. \(x^2-169=(x+13)(x-13)\)
10. \(4x^{14}-169=(2x^7+13)(2x^7-13)\)
11. \(q^2-12q+36=(q-6)^2\)
12. \(9-256p^{10}=(3-16p^5)(3+16p^5)\)