Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(196a^{10}+28a^5+1\)
2. \(225-196b^{12}\)
3. \(1-100y^{10}\)
4. \(100q^2-260q+169\)
5. \(p^2-36\)
6. \(25b^{10}-90b^5s+81s^2\)
7. \(121s^{6}-154s^3y+49y^2\)
8. \(b^2+12b+36\)
9. \(4q^2-9p^{6}\)
10. \(49s^{8}-225\)
11. \(-9x^2+16\)
12. \(196-169a^{4}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(196a^{10}+28a^5+1=(14a^5+1)^2\)
2. \(225-196b^{12}=(15-14b^6)(15+14b^6)\)
3. \(1-100y^{10}=(1-10y^5)(1+10y^5)\)
4. \(100q^2-260q+169=(10q-13)^2\)
5. \(p^2-36=(p+6)(p-6)\)
6. \(25b^{10}-90b^5s+81s^2=(5b^5-9s)^2\)
7. \(121s^{6}-154s^3y+49y^2=(11s^3-7y)^2\)
8. \(b^2+12b+36=(b+6)^2\)
9. \(4q^2-9p^{6}=(2q-3p^3)(2q+3p^3)\)
10. \(49s^{8}-225=(7s^4+15)(7s^4-15)\)
11. \(-9x^2+16=(4-3x)(4+3x)\)
12. \(196-169a^{4}=(14-13a^2)(14+13a^2)\)