Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(36a^{16}-121p^2\)
2. \(a^2-30a+225\)
3. \(49y^2-100\)
4. \(100a^{4}+140a^2q+49q^2\)
5. \(p^2-100\)
6. \(y^2+2y+1\)
7. \(4q^2-225b^{8}\)
8. \(225s^2+330s+121\)
9. \(36b^2-49\)
10. \(b^2-4\)
11. \(81b^{10}+180b^5q+100q^2\)
12. \(49p^{10}-224p^5+256\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(36a^{16}-121p^2=(6a^8+11p)(6a^8-11p)\)
2. \(a^2-30a+225=(a-15)^2\)
3. \(49y^2-100=(7y+10)(7y-10)\)
4. \(100a^{4}+140a^2q+49q^2=(10a^2+7q)^2\)
5. \(p^2-100=(p-10)(p+10)\)
6. \(y^2+2y+1=(y+1)^2\)
7. \(4q^2-225b^{8}=(2q-15b^4)(2q+15b^4)\)
8. \(225s^2+330s+121=(15s+11)^2\)
9. \(36b^2-49=(6b+7)(6b-7)\)
10. \(b^2-4=(b+2)(b-2)\)
11. \(81b^{10}+180b^5q+100q^2=(9b^5+10q)^2\)
12. \(49p^{10}-224p^5+256=(7p^5-16)^2\)