Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(256a^{8}-480a^4p+225p^2\)
2. \(225y^{6}-60y^3+4\)
3. \(100s^{6}+140s^3y+49y^2\)
4. \(256a^2+288a+81\)
5. \(36s^{8}-132s^4+121\)
6. \(a^2-196\)
7. \(4p^{4}-169s^2\)
8. \(25p^2-36\)
9. \(121y^2-4x^{16}\)
10. \(4a^{6}-225q^2\)
11. \(16p^{10}+120p^5+225\)
12. \(s^2+4s+4\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(256a^{8}-480a^4p+225p^2=(16a^4-15p)^2\)
2. \(225y^{6}-60y^3+4=(15y^3-2)^2\)
3. \(100s^{6}+140s^3y+49y^2=(10s^3+7y)^2\)
4. \(256a^2+288a+81=(16a+9)^2\)
5. \(36s^{8}-132s^4+121=(6s^4-11)^2\)
6. \(a^2-196=(a-14)(a+14)\)
7. \(4p^{4}-169s^2=(2p^2+13s)(2p^2-13s)\)
8. \(25p^2-36=(5p+6)(5p-6)\)
9. \(121y^2-4x^{16}=(11y-2x^8)(11y+2x^8)\)
10. \(4a^{6}-225q^2=(2a^3+15q)(2a^3-15q)\)
11. \(16p^{10}+120p^5+225=(4p^5+15)^2\)
12. \(s^2+4s+4=(s+2)^2\)