Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(169p^2+364p+196\)
2. \(4x^{8}-169\)
3. \(-64x^2+225\)
4. \(256x^2-9\)
5. \(a^2-36\)
6. \(196b^2-169a^{8}\)
7. \(p^2-22p+121\)
8. \(-36q^2+49\)
9. \(100p^{12}-1\)
10. \(144p^{4}+120p^2+25\)
11. \(b^2-1\)
12. \(196p^{4}+252p^2+81\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(169p^2+364p+196=(13p+14)^2\)
2. \(4x^{8}-169=(2x^4+13)(2x^4-13)\)
3. \(-64x^2+225=(15-8x)(15+8x)\)
4. \(256x^2-9=(16x+3)(16x-3)\)
5. \(a^2-36=(a-6)(a+6)\)
6. \(196b^2-169a^{8}=(14b-13a^4)(14b+13a^4)\)
7. \(p^2-22p+121=(p-11)^2\)
8. \(-36q^2+49=(7-6q)(7+6q)\)
9. \(100p^{12}-1=(10p^6+1)(10p^6-1)\)
10. \(144p^{4}+120p^2+25=(12p^2+5)^2\)
11. \(b^2-1=(b+1)(b-1)\)
12. \(196p^{4}+252p^2+81=(14p^2+9)^2\)