Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(a^2+2a+1\)
2. \(x^2+14x+49\)
3. \(16a^{6}-88a^3q+121q^2\)
4. \(121a^2-1\)
5. \(100x^2+220x+121\)
6. \(100b^{4}+140b^2+49\)
7. \(p^2-4\)
8. \(121a^2-220a+100\)
9. \(121x^2-4p^{12}\)
10. \(s^2-225\)
11. \(225p^{14}-4s^2\)
12. \(49x^{6}+56x^3+16\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(a^2+2a+1=(a+1)^2\)
2. \(x^2+14x+49=(x+7)^2\)
3. \(16a^{6}-88a^3q+121q^2=(4a^3-11q)^2\)
4. \(121a^2-1=(11a+1)(11a-1)\)
5. \(100x^2+220x+121=(10x+11)^2\)
6. \(100b^{4}+140b^2+49=(10b^2+7)^2\)
7. \(p^2-4=(p+2)(p-2)\)
8. \(121a^2-220a+100=(11a-10)^2\)
9. \(121x^2-4p^{12}=(11x-2p^6)(11x+2p^6)\)
10. \(s^2-225=(s-15)(s+15)\)
11. \(225p^{14}-4s^2=(15p^7+2s)(15p^7-2s)\)
12. \(49x^{6}+56x^3+16=(7x^3+4)^2\)