Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(144p^{4}-264p^2y+121y^2\)
2. \(25q^2-90q+81\)
3. \(100y^{14}-49\)
4. \(100a^{8}-260a^4p+169p^2\)
5. \(25b^{6}+60b^3x+36x^2\)
6. \(9a^{6}-84a^3q+196q^2\)
7. \(q^2+10q+25\)
8. \(64b^{6}-121q^2\)
9. \(64p^{4}+80p^2+25\)
10. \(s^2-4\)
11. \(q^2-16\)
12. \(64x^{4}-25\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(144p^{4}-264p^2y+121y^2=(12p^2-11y)^2\)
2. \(25q^2-90q+81=(5q-9)^2\)
3. \(100y^{14}-49=(10y^7+7)(10y^7-7)\)
4. \(100a^{8}-260a^4p+169p^2=(10a^4-13p)^2\)
5. \(25b^{6}+60b^3x+36x^2=(5b^3+6x)^2\)
6. \(9a^{6}-84a^3q+196q^2=(3a^3-14q)^2\)
7. \(q^2+10q+25=(q+5)^2\)
8. \(64b^{6}-121q^2=(8b^3+11q)(8b^3-11q)\)
9. \(64p^{4}+80p^2+25=(8p^2+5)^2\)
10. \(s^2-4=(s+2)(s-2)\)
11. \(q^2-16=(q-4)(q+4)\)
12. \(64x^{4}-25=(8x^2+5)(8x^2-5)\)