Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25x^{10}-70x^5+49\)
2. \(b^2-9\)
3. \(a^2+12a+36\)
4. \(225x^{6}-420x^3+196\)
5. \(a^2+8a+16\)
6. \(81x^2-234x+169\)
7. \(196q^2-9\)
8. \(81x^{6}-72x^3+16\)
9. \(100y^2-121a^{12}\)
10. \(100b^{4}-180b^2+81\)
11. \(100x^2+140x+49\)
12. \(225s^{10}-49\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25x^{10}-70x^5+49=(5x^5-7)^2\)
2. \(b^2-9=(b+3)(b-3)\)
3. \(a^2+12a+36=(a+6)^2\)
4. \(225x^{6}-420x^3+196=(15x^3-14)^2\)
5. \(a^2+8a+16=(a+4)^2\)
6. \(81x^2-234x+169=(9x-13)^2\)
7. \(196q^2-9=(14q+3)(14q-3)\)
8. \(81x^{6}-72x^3+16=(9x^3-4)^2\)
9. \(100y^2-121a^{12}=(10y-11a^6)(10y+11a^6)\)
10. \(100b^{4}-180b^2+81=(10b^2-9)^2\)
11. \(100x^2+140x+49=(10x+7)^2\)
12. \(225s^{10}-49=(15s^5+7)(15s^5-7)\)