Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(225x^{10}-169y^2\)
2. \(y^2-36\)
3. \(b^2-225\)
4. \(81a^{10}+144a^5p+64p^2\)
5. \(y^2-49\)
6. \(q^2-24q+144\)
7. \(225b^{8}-330b^4q+121q^2\)
8. \(25a^{8}+80a^4x+64x^2\)
9. \(64x^2-121\)
10. \(a^2+2a+1\)
11. \(81p^2-121a^{10}\)
12. \(b^2-20b+100\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(225x^{10}-169y^2=(15x^5+13y)(15x^5-13y)\)
2. \(y^2-36=(y+6)(y-6)\)
3. \(b^2-225=(b+15)(b-15)\)
4. \(81a^{10}+144a^5p+64p^2=(9a^5+8p)^2\)
5. \(y^2-49=(y-7)(y+7)\)
6. \(q^2-24q+144=(q-12)^2\)
7. \(225b^{8}-330b^4q+121q^2=(15b^4-11q)^2\)
8. \(25a^{8}+80a^4x+64x^2=(5a^4+8x)^2\)
9. \(64x^2-121=(8x+11)(8x-11)\)
10. \(a^2+2a+1=(a+1)^2\)
11. \(81p^2-121a^{10}=(9p-11a^5)(9p+11a^5)\)
12. \(b^2-20b+100=(b-10)^2\)