Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(16-225p^{16}\)
2. \(144q^{8}+264q^4+121\)
3. \(144q^2-169\)
4. \(a^2+4a+4\)
5. \(4a^{10}+4a^5x+1x^2\)
6. \(9p^{8}+6p^4+1\)
7. \(y^2-2y+1\)
8. \(256x^{4}-480x^2y+225y^2\)
9. \(4q^{10}-169y^2\)
10. \(49y^2+210y+225\)
11. \(4b^{10}-49x^2\)
12. \(64p^{4}+144p^2+81\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(16-225p^{16}=(4-15p^8)(4+15p^8)\)
2. \(144q^{8}+264q^4+121=(12q^4+11)^2\)
3. \(144q^2-169=(12q+13)(12q-13)\)
4. \(a^2+4a+4=(a+2)^2\)
5. \(4a^{10}+4a^5x+1x^2=(2a^5+x)^2\)
6. \(9p^{8}+6p^4+1=(3p^4+1)^2\)
7. \(y^2-2y+1=(y-1)^2\)
8. \(256x^{4}-480x^2y+225y^2=(16x^2-15y)^2\)
9. \(4q^{10}-169y^2=(2q^5+13y)(2q^5-13y)\)
10. \(49y^2+210y+225=(7y+15)^2\)
11. \(4b^{10}-49x^2=(2b^5+7x)(2b^5-7x)\)
12. \(64p^{4}+144p^2+81=(8p^2+9)^2\)