Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(4b^{10}+28b^5x+49x^2\)
2. \(49a^2-100\)
3. \(-169a^2+225\)
4. \(81p^2-234p+169\)
5. \(16p^2-225a^{6}\)
6. \(y^2-4y+4\)
7. \(100s^{8}-180s^4+81\)
8. \(q^2-18q+81\)
9. \(225a^2+30a+1\)
10. \(169y^2-144x^{10}\)
11. \(x^2-10x+25\)
12. \(36p^{10}-132p^5+121\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(4b^{10}+28b^5x+49x^2=(2b^5+7x)^2\)
2. \(49a^2-100=(7a+10)(7a-10)\)
3. \(-169a^2+225=(15-13a)(15+13a)\)
4. \(81p^2-234p+169=(9p-13)^2\)
5. \(16p^2-225a^{6}=(4p-15a^3)(4p+15a^3)\)
6. \(y^2-4y+4=(y-2)^2\)
7. \(100s^{8}-180s^4+81=(10s^4-9)^2\)
8. \(q^2-18q+81=(q-9)^2\)
9. \(225a^2+30a+1=(15a+1)^2\)
10. \(169y^2-144x^{10}=(13y-12x^5)(13y+12x^5)\)
11. \(x^2-10x+25=(x-5)^2\)
12. \(36p^{10}-132p^5+121=(6p^5-11)^2\)