Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25q^{10}-4y^2\)
2. \(a^{4}-36x^2\)
3. \(p^2-36\)
4. \(9-25a^{4}\)
5. \(49s^2-225\)
6. \(-16b^2+81\)
7. \(y^2-22y+121\)
8. \(25b^{4}-40b^2q+16q^2\)
9. \(49s^{6}-225y^2\)
10. \(-196x^2+169\)
11. \(b^2-1\)
12. \(169y^2-390y+225\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25q^{10}-4y^2=(5q^5+2y)(5q^5-2y)\)
2. \(a^{4}-36x^2=(a^2+6x)(a^2-6x)\)
3. \(p^2-36=(p+6)(p-6)\)
4. \(9-25a^{4}=(3-5a^2)(3+5a^2)\)
5. \(49s^2-225=(7s+15)(7s-15)\)
6. \(-16b^2+81=(9-4b)(9+4b)\)
7. \(y^2-22y+121=(y-11)^2\)
8. \(25b^{4}-40b^2q+16q^2=(5b^2-4q)^2\)
9. \(49s^{6}-225y^2=(7s^3+15y)(7s^3-15y)\)
10. \(-196x^2+169=(13-14x)(13+14x)\)
11. \(b^2-1=(b-1)(b+1)\)
12. \(169y^2-390y+225=(13y-15)^2\)