Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(1-25x^{6}\)
2. \(s^2-49\)
3. \(25q^2-36p^{16}\)
4. \(49a^{12}-36\)
5. \(9b^2-30b+25\)
6. \(256a^{8}-169s^2\)
7. \(s^2+10s+25\)
8. \(49x^{8}-100\)
9. \(25p^{10}+140p^5s+196s^2\)
10. \(-121q^2+1\)
11. \(4q^{4}+60q^2+225\)
12. \(121b^{12}-100q^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(1-25x^{6}=(1-5x^3)(1+5x^3)\)
2. \(s^2-49=(s-7)(s+7)\)
3. \(25q^2-36p^{16}=(5q-6p^8)(5q+6p^8)\)
4. \(49a^{12}-36=(7a^6+6)(7a^6-6)\)
5. \(9b^2-30b+25=(3b-5)^2\)
6. \(256a^{8}-169s^2=(16a^4+13s)(16a^4-13s)\)
7. \(s^2+10s+25=(s+5)^2\)
8. \(49x^{8}-100=(7x^4+10)(7x^4-10)\)
9. \(25p^{10}+140p^5s+196s^2=(5p^5+14s)^2\)
10. \(-121q^2+1=(1-11q)(1+11q)\)
11. \(4q^{4}+60q^2+225=(2q^2+15)^2\)
12. \(121b^{12}-100q^2=(11b^6+10q)(11b^6-10q)\)