Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25b^{4}-1\)
2. \(64b^{8}+240b^4+225\)
3. \(121p^{12}-144\)
4. \(25p^{6}+10p^3+1\)
5. \(y^2-225\)
6. \(9s^2+24s+16\)
7. \(x^2+8x+16\)
8. \(64x^{10}+240x^5y+225y^2\)
9. \(-4p^2+9\)
10. \(y^2-10y+25\)
11. \(25-121p^{12}\)
12. \(64y^2-81a^{12}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25b^{4}-1=(5b^2+1)(5b^2-1)\)
2. \(64b^{8}+240b^4+225=(8b^4+15)^2\)
3. \(121p^{12}-144=(11p^6+12)(11p^6-12)\)
4. \(25p^{6}+10p^3+1=(5p^3+1)^2\)
5. \(y^2-225=(y-15)(y+15)\)
6. \(9s^2+24s+16=(3s+4)^2\)
7. \(x^2+8x+16=(x+4)^2\)
8. \(64x^{10}+240x^5y+225y^2=(8x^5+15y)^2\)
9. \(-4p^2+9=(3-2p)(3+2p)\)
10. \(y^2-10y+25=(y-5)^2\)
11. \(25-121p^{12}=(5-11p^6)(5+11p^6)\)
12. \(64y^2-81a^{12}=(8y-9a^6)(8y+9a^6)\)