Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(p^2+4p+4\)
2. \(25x^{4}-36\)
3. \(16s^{10}-56s^5y+49y^2\)
4. \(121-144p^{6}\)
5. \(b^2-30b+225\)
6. \(81b^{12}-4y^2\)
7. \(196y^{8}+308y^4+121\)
8. \(25y^{4}+40y^2+16\)
9. \(100-49q^{6}\)
10. \(-64a^2+169\)
11. \(169q^{8}-312q^4x+144x^2\)
12. \(49p^2-100a^{6}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(p^2+4p+4=(p+2)^2\)
2. \(25x^{4}-36=(5x^2+6)(5x^2-6)\)
3. \(16s^{10}-56s^5y+49y^2=(4s^5-7y)^2\)
4. \(121-144p^{6}=(11-12p^3)(11+12p^3)\)
5. \(b^2-30b+225=(b-15)^2\)
6. \(81b^{12}-4y^2=(9b^6+2y)(9b^6-2y)\)
7. \(196y^{8}+308y^4+121=(14y^4+11)^2\)
8. \(25y^{4}+40y^2+16=(5y^2+4)^2\)
9. \(100-49q^{6}=(10-7q^3)(10+7q^3)\)
10. \(-64a^2+169=(13-8a)(13+8a)\)
11. \(169q^{8}-312q^4x+144x^2=(13q^4-12x)^2\)
12. \(49p^2-100a^{6}=(7p-10a^3)(7p+10a^3)\)