Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(q^2-30q+225\)
2. \(25q^{16}-36y^2\)
3. \(36q^{6}-1\)
4. \(-25y^2+16\)
5. \(25q^2-144b^{8}\)
6. \(121-9b^{12}\)
7. \(16x^{6}-88x^3+121\)
8. \(196q^{4}+364q^2y+169y^2\)
9. \(a^2-225\)
10. \(s^2-121\)
11. \(9s^2-196b^{6}\)
12. \(49y^2-100b^{6}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(q^2-30q+225=(q-15)^2\)
2. \(25q^{16}-36y^2=(5q^8+6y)(5q^8-6y)\)
3. \(36q^{6}-1=(6q^3+1)(6q^3-1)\)
4. \(-25y^2+16=(4-5y)(4+5y)\)
5. \(25q^2-144b^{8}=(5q-12b^4)(5q+12b^4)\)
6. \(121-9b^{12}=(11-3b^6)(11+3b^6)\)
7. \(16x^{6}-88x^3+121=(4x^3-11)^2\)
8. \(196q^{4}+364q^2y+169y^2=(14q^2+13y)^2\)
9. \(a^2-225=(a-15)(a+15)\)
10. \(s^2-121=(s+11)(s-11)\)
11. \(9s^2-196b^{6}=(3s-14b^3)(3s+14b^3)\)
12. \(49y^2-100b^{6}=(7y-10b^3)(7y+10b^3)\)