Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25a^{10}+110a^5+121\)
2. \(256a^{4}-160a^2x+25x^2\)
3. \(49q^2-182q+169\)
4. \(p^2-24p+144\)
5. \(121p^{6}-144q^2\)
6. \(q^2-30q+225\)
7. \(9y^{6}-169\)
8. \(64p^2-112p+49\)
9. \(121y^{6}-44y^3+4\)
10. \(-256p^2+25\)
11. \(9a^2-121\)
12. \(y^2-196\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25a^{10}+110a^5+121=(5a^5+11)^2\)
2. \(256a^{4}-160a^2x+25x^2=(16a^2-5x)^2\)
3. \(49q^2-182q+169=(7q-13)^2\)
4. \(p^2-24p+144=(p-12)^2\)
5. \(121p^{6}-144q^2=(11p^3+12q)(11p^3-12q)\)
6. \(q^2-30q+225=(q-15)^2\)
7. \(9y^{6}-169=(3y^3+13)(3y^3-13)\)
8. \(64p^2-112p+49=(8p-7)^2\)
9. \(121y^{6}-44y^3+4=(11y^3-2)^2\)
10. \(-256p^2+25=(5-16p)(5+16p)\)
11. \(9a^2-121=(3a+11)(3a-11)\)
12. \(y^2-196=(y+14)(y-14)\)