Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(81p^2-25a^{10}\)
2. \(x^2-4x+4\)
3. \(25y^2-36b^{16}\)
4. \(36s^2+12s+1\)
5. \(25p^{10}+70p^5s+49s^2\)
6. \(16q^{8}-169\)
7. \(225q^2+60q+4\)
8. \(144b^{4}+168b^2q+49q^2\)
9. \(121y^2-286y+169\)
10. \(256s^{8}+32s^4y+1y^2\)
11. \(b^{4}-49q^2\)
12. \(196b^{6}-364b^3s+169s^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(81p^2-25a^{10}=(9p-5a^5)(9p+5a^5)\)
2. \(x^2-4x+4=(x-2)^2\)
3. \(25y^2-36b^{16}=(5y-6b^8)(5y+6b^8)\)
4. \(36s^2+12s+1=(6s+1)^2\)
5. \(25p^{10}+70p^5s+49s^2=(5p^5+7s)^2\)
6. \(16q^{8}-169=(4q^4+13)(4q^4-13)\)
7. \(225q^2+60q+4=(15q+2)^2\)
8. \(144b^{4}+168b^2q+49q^2=(12b^2+7q)^2\)
9. \(121y^2-286y+169=(11y-13)^2\)
10. \(256s^{8}+32s^4y+1y^2=(16s^4+y)^2\)
11. \(b^{4}-49q^2=(b^2+7q)(b^2-7q)\)
12. \(196b^{6}-364b^3s+169s^2=(14b^3-13s)^2\)