Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(49p^{12}-225y^2\)
2. \(x^2-30x+225\)
3. \(64s^2-49b^{14}\)
4. \(b^2+24b+144\)
5. \(196p^{10}+364p^5q+169q^2\)
6. \(25q^{6}-140q^3x+196x^2\)
7. \(81p^2-100\)
8. \(256y^{8}-121\)
9. \(49s^{4}-182s^2+169\)
10. \(100p^{10}+20p^5+1\)
11. \(25-49a^{6}\)
12. \(a^{6}-256p^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(49p^{12}-225y^2=(7p^6+15y)(7p^6-15y)\)
2. \(x^2-30x+225=(x-15)^2\)
3. \(64s^2-49b^{14}=(8s-7b^7)(8s+7b^7)\)
4. \(b^2+24b+144=(b+12)^2\)
5. \(196p^{10}+364p^5q+169q^2=(14p^5+13q)^2\)
6. \(25q^{6}-140q^3x+196x^2=(5q^3-14x)^2\)
7. \(81p^2-100=(9p+10)(9p-10)\)
8. \(256y^{8}-121=(16y^4+11)(16y^4-11)\)
9. \(49s^{4}-182s^2+169=(7s^2-13)^2\)
10. \(100p^{10}+20p^5+1=(10p^5+1)^2\)
11. \(25-49a^{6}=(5-7a^3)(5+7a^3)\)
12. \(a^{6}-256p^2=(a^3+16p)(a^3-16p)\)