Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25q^{4}-40q^2+16\)
2. \(9q^2-84q+196\)
3. \(36q^{6}+156q^3+169\)
4. \(25s^{8}-120s^4x+144x^2\)
5. \(256a^{8}+480a^4p+225p^2\)
6. \(256b^2+32b+1\)
7. \(b^2-26b+169\)
8. \(169q^2-49\)
9. \(169p^{16}-144x^2\)
10. \(100p^{4}-49q^2\)
11. \(4b^2-225\)
12. \(121q^2-144b^{12}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25q^{4}-40q^2+16=(5q^2-4)^2\)
2. \(9q^2-84q+196=(3q-14)^2\)
3. \(36q^{6}+156q^3+169=(6q^3+13)^2\)
4. \(25s^{8}-120s^4x+144x^2=(5s^4-12x)^2\)
5. \(256a^{8}+480a^4p+225p^2=(16a^4+15p)^2\)
6. \(256b^2+32b+1=(16b+1)^2\)
7. \(b^2-26b+169=(b-13)^2\)
8. \(169q^2-49=(13q+7)(13q-7)\)
9. \(169p^{16}-144x^2=(13p^8+12x)(13p^8-12x)\)
10. \(100p^{4}-49q^2=(10p^2+7q)(10p^2-7q)\)
11. \(4b^2-225=(2b+15)(2b-15)\)
12. \(121q^2-144b^{12}=(11q-12b^6)(11q+12b^6)\)