Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(81b^2-72b+16\)
2. \(25p^{10}-40p^5+16\)
3. \(225a^{8}-60a^4b+4b^2\)
4. \(25q^2-144b^{4}\)
5. \(16b^{4}-1\)
6. \(p^2-10p+25\)
7. \(9s^{4}-84s^2+196\)
8. \(225p^{4}-49y^2\)
9. \(81y^{4}-198y^2+121\)
10. \(-49y^2+1\)
11. \(a^2-22a+121\)
12. \(a^2-30a+225\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(81b^2-72b+16=(9b-4)^2\)
2. \(25p^{10}-40p^5+16=(5p^5-4)^2\)
3. \(225a^{8}-60a^4b+4b^2=(15a^4-2b)^2\)
4. \(25q^2-144b^{4}=(5q-12b^2)(5q+12b^2)\)
5. \(16b^{4}-1=(4b^2+1)(4b^2-1)\)
6. \(p^2-10p+25=(p-5)^2\)
7. \(9s^{4}-84s^2+196=(3s^2-14)^2\)
8. \(225p^{4}-49y^2=(15p^2+7y)(15p^2-7y)\)
9. \(81y^{4}-198y^2+121=(9y^2-11)^2\)
10. \(-49y^2+1=(1-7y)(1+7y)\)
11. \(a^2-22a+121=(a-11)^2\)
12. \(a^2-30a+225=(a-15)^2\)