Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(49x^{6}-28x^3+4\)
2. \(4q^2-9p^{6}\)
3. \(q^2-14q+49\)
4. \(b^2-64\)
5. \(100b^{8}+140b^4x+49x^2\)
6. \(p^2+12p+36\)
7. \(25-64b^{14}\)
8. \(121y^2-44y+4\)
9. \(s^2-20s+100\)
10. \(q^{4}-100y^2\)
11. \(a^2+28a+196\)
12. \(100a^{14}-9x^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(49x^{6}-28x^3+4=(7x^3-2)^2\)
2. \(4q^2-9p^{6}=(2q-3p^3)(2q+3p^3)\)
3. \(q^2-14q+49=(q-7)^2\)
4. \(b^2-64=(b-8)(b+8)\)
5. \(100b^{8}+140b^4x+49x^2=(10b^4+7x)^2\)
6. \(p^2+12p+36=(p+6)^2\)
7. \(25-64b^{14}=(5-8b^7)(5+8b^7)\)
8. \(121y^2-44y+4=(11y-2)^2\)
9. \(s^2-20s+100=(s-10)^2\)
10. \(q^{4}-100y^2=(q^2+10y)(q^2-10y)\)
11. \(a^2+28a+196=(a+14)^2\)
12. \(100a^{14}-9x^2=(10a^7+3x)(10a^7-3x)\)