Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(9p^2-66p+121\)
2. \(a^2-4\)
3. \(100p^2-1\)
4. \(a^2-81\)
5. \(4p^{10}+4p^5q+1q^2\)
6. \(25x^2-81q^{14}\)
7. \(169a^{6}-196q^2\)
8. \(36b^2-60b+25\)
9. \(196q^{12}-81x^2\)
10. \(36x^2+84x+49\)
11. \(196-169a^{8}\)
12. \(9-121y^{8}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(9p^2-66p+121=(3p-11)^2\)
2. \(a^2-4=(a+2)(a-2)\)
3. \(100p^2-1=(10p+1)(10p-1)\)
4. \(a^2-81=(a+9)(a-9)\)
5. \(4p^{10}+4p^5q+1q^2=(2p^5+q)^2\)
6. \(25x^2-81q^{14}=(5x-9q^7)(5x+9q^7)\)
7. \(169a^{6}-196q^2=(13a^3+14q)(13a^3-14q)\)
8. \(36b^2-60b+25=(6b-5)^2\)
9. \(196q^{12}-81x^2=(14q^6+9x)(14q^6-9x)\)
10. \(36x^2+84x+49=(6x+7)^2\)
11. \(196-169a^{8}=(14-13a^4)(14+13a^4)\)
12. \(9-121y^{8}=(3-11y^4)(3+11y^4)\)