Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(169a^2-312a+144\)
2. \(81-196y^{14}\)
3. \(x^2-121\)
4. \(4b^2+4b+1\)
5. \(100x^{14}-169\)
6. \(16p^2-121\)
7. \(196q^{4}+420q^2+225\)
8. \(196q^{4}+84q^2s+9s^2\)
9. \(p^2-8p+16\)
10. \(81p^2-49b^{4}\)
11. \(25s^{10}-36\)
12. \(49b^{10}+56b^5+16\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(169a^2-312a+144=(13a-12)^2\)
2. \(81-196y^{14}=(9-14y^7)(9+14y^7)\)
3. \(x^2-121=(x+11)(x-11)\)
4. \(4b^2+4b+1=(2b+1)^2\)
5. \(100x^{14}-169=(10x^7+13)(10x^7-13)\)
6. \(16p^2-121=(4p+11)(4p-11)\)
7. \(196q^{4}+420q^2+225=(14q^2+15)^2\)
8. \(196q^{4}+84q^2s+9s^2=(14q^2+3s)^2\)
9. \(p^2-8p+16=(p-4)^2\)
10. \(81p^2-49b^{4}=(9p-7b^2)(9p+7b^2)\)
11. \(25s^{10}-36=(5s^5+6)(5s^5-6)\)
12. \(49b^{10}+56b^5+16=(7b^5+4)^2\)