Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25x^{6}+120x^3y+144y^2\)
2. \(s^2-100\)
3. \(49-4q^{10}\)
4. \(b^2-225\)
5. \(36s^{8}-132s^4x+121x^2\)
6. \(1-25q^{4}\)
7. \(49p^{10}+14p^5+1\)
8. \(121-100y^{10}\)
9. \(100b^{4}-60b^2y+9y^2\)
10. \(9p^{6}-12p^3y+4y^2\)
11. \(100q^{10}-180q^5s+81s^2\)
12. \(p^2-12p+36\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25x^{6}+120x^3y+144y^2=(5x^3+12y)^2\)
2. \(s^2-100=(s+10)(s-10)\)
3. \(49-4q^{10}=(7-2q^5)(7+2q^5)\)
4. \(b^2-225=(b-15)(b+15)\)
5. \(36s^{8}-132s^4x+121x^2=(6s^4-11x)^2\)
6. \(1-25q^{4}=(1-5q^2)(1+5q^2)\)
7. \(49p^{10}+14p^5+1=(7p^5+1)^2\)
8. \(121-100y^{10}=(11-10y^5)(11+10y^5)\)
9. \(100b^{4}-60b^2y+9y^2=(10b^2-3y)^2\)
10. \(9p^{6}-12p^3y+4y^2=(3p^3-2y)^2\)
11. \(100q^{10}-180q^5s+81s^2=(10q^5-9s)^2\)
12. \(p^2-12p+36=(p-6)^2\)