Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(49y^2-121b^{14}\)
2. \(16x^{10}-225y^2\)
3. \(49b^{8}-42b^4+9\)
4. \(256b^{10}+480b^5y+225y^2\)
5. \(100p^{8}-180p^4q+81q^2\)
6. \(s^2-16\)
7. \(x^2+30x+225\)
8. \(100s^{4}+260s^2+169\)
9. \(q^2-1\)
10. \(a^2+8a+16\)
11. \(121b^{8}-9\)
12. \(144b^{10}+312b^5+169\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(49y^2-121b^{14}=(7y-11b^7)(7y+11b^7)\)
2. \(16x^{10}-225y^2=(4x^5+15y)(4x^5-15y)\)
3. \(49b^{8}-42b^4+9=(7b^4-3)^2\)
4. \(256b^{10}+480b^5y+225y^2=(16b^5+15y)^2\)
5. \(100p^{8}-180p^4q+81q^2=(10p^4-9q)^2\)
6. \(s^2-16=(s+4)(s-4)\)
7. \(x^2+30x+225=(x+15)^2\)
8. \(100s^{4}+260s^2+169=(10s^2+13)^2\)
9. \(q^2-1=(q-1)(q+1)\)
10. \(a^2+8a+16=(a+4)^2\)
11. \(121b^{8}-9=(11b^4+3)(11b^4-3)\)
12. \(144b^{10}+312b^5+169=(12b^5+13)^2\)