Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(81y^2-196\)
2. \(a^2+14a+49\)
3. \(196p^2+84p+9\)
4. \(49b^{6}+14b^3+1\)
5. \(x^2-8x+16\)
6. \(256a^{12}-81p^2\)
7. \(16b^{10}-120b^5x+225x^2\)
8. \(y^2-225\)
9. \(1-4s^{14}\)
10. \(25x^{10}-1\)
11. \(100y^2-169\)
12. \(25s^{4}-140s^2+196\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(81y^2-196=(9y+14)(9y-14)\)
2. \(a^2+14a+49=(a+7)^2\)
3. \(196p^2+84p+9=(14p+3)^2\)
4. \(49b^{6}+14b^3+1=(7b^3+1)^2\)
5. \(x^2-8x+16=(x-4)^2\)
6. \(256a^{12}-81p^2=(16a^6+9p)(16a^6-9p)\)
7. \(16b^{10}-120b^5x+225x^2=(4b^5-15x)^2\)
8. \(y^2-225=(y-15)(y+15)\)
9. \(1-4s^{14}=(1-2s^7)(1+2s^7)\)
10. \(25x^{10}-1=(5x^5+1)(5x^5-1)\)
11. \(100y^2-169=(10y+13)(10y-13)\)
12. \(25s^{4}-140s^2+196=(5s^2-14)^2\)