Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(64b^{6}-25q^2\)
2. \(144b^2-25\)
3. \(256a^2+32a+1\)
4. \(16b^{12}-225q^2\)
5. \(100x^{10}+180x^5+81\)
6. \(-16y^2+1\)
7. \(169-100b^{12}\)
8. \(81q^2-256p^{6}\)
9. \(121b^{8}-25\)
10. \(64p^{4}-112p^2x+49x^2\)
11. \(p^2-8p+16\)
12. \(81x^{4}-36x^2+4\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(64b^{6}-25q^2=(8b^3+5q)(8b^3-5q)\)
2. \(144b^2-25=(12b+5)(12b-5)\)
3. \(256a^2+32a+1=(16a+1)^2\)
4. \(16b^{12}-225q^2=(4b^6+15q)(4b^6-15q)\)
5. \(100x^{10}+180x^5+81=(10x^5+9)^2\)
6. \(-16y^2+1=(1-4y)(1+4y)\)
7. \(169-100b^{12}=(13-10b^6)(13+10b^6)\)
8. \(81q^2-256p^{6}=(9q-16p^3)(9q+16p^3)\)
9. \(121b^{8}-25=(11b^4+5)(11b^4-5)\)
10. \(64p^{4}-112p^2x+49x^2=(8p^2-7x)^2\)
11. \(p^2-8p+16=(p-4)^2\)
12. \(81x^{4}-36x^2+4=(9x^2-2)^2\)