Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25p^{4}-70p^2+49\)
2. \(4y^{4}+4y^2+1\)
3. \(y^2-64\)
4. \(a^2-16\)
5. \(121q^2-1\)
6. \(16a^{10}+104a^5y+169y^2\)
7. \(16-225q^{4}\)
8. \(121-225p^{16}\)
9. \(s^2-144\)
10. \(121y^2-25a^{8}\)
11. \(25p^{4}-20p^2q+4q^2\)
12. \(p^2-49\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25p^{4}-70p^2+49=(5p^2-7)^2\)
2. \(4y^{4}+4y^2+1=(2y^2+1)^2\)
3. \(y^2-64=(y-8)(y+8)\)
4. \(a^2-16=(a+4)(a-4)\)
5. \(121q^2-1=(11q+1)(11q-1)\)
6. \(16a^{10}+104a^5y+169y^2=(4a^5+13y)^2\)
7. \(16-225q^{4}=(4-15q^2)(4+15q^2)\)
8. \(121-225p^{16}=(11-15p^8)(11+15p^8)\)
9. \(s^2-144=(s-12)(s+12)\)
10. \(121y^2-25a^{8}=(11y-5a^4)(11y+5a^4)\)
11. \(25p^{4}-20p^2q+4q^2=(5p^2-2q)^2\)
12. \(p^2-49=(p+7)(p-7)\)