Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(256a^{4}-160a^2+25\)
2. \(49-36s^{8}\)
3. \(s^2+8s+16\)
4. \(16p^{10}+56p^5+49\)
5. \(49b^{10}-121\)
6. \(-100x^2+121\)
7. \(100a^2+220a+121\)
8. \(121x^{4}-220x^2+100\)
9. \(81q^{12}-25s^2\)
10. \(121a^{4}-16x^2\)
11. \(49x^2-225\)
12. \(1-25p^{8}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(256a^{4}-160a^2+25=(16a^2-5)^2\)
2. \(49-36s^{8}=(7-6s^4)(7+6s^4)\)
3. \(s^2+8s+16=(s+4)^2\)
4. \(16p^{10}+56p^5+49=(4p^5+7)^2\)
5. \(49b^{10}-121=(7b^5+11)(7b^5-11)\)
6. \(-100x^2+121=(11-10x)(11+10x)\)
7. \(100a^2+220a+121=(10a+11)^2\)
8. \(121x^{4}-220x^2+100=(11x^2-10)^2\)
9. \(81q^{12}-25s^2=(9q^6+5s)(9q^6-5s)\)
10. \(121a^{4}-16x^2=(11a^2+4x)(11a^2-4x)\)
11. \(49x^2-225=(7x+15)(7x-15)\)
12. \(1-25p^{8}=(1-5p^4)(1+5p^4)\)