Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(256b^{10}+160b^5p+25p^2\)
2. \(1-64b^{4}\)
3. \(49a^{4}-25s^2\)
4. \(4y^2-25b^{14}\)
5. \(y^2+30y+225\)
6. \(144a^{8}-264a^4b+121b^2\)
7. \(81y^{10}-4\)
8. \(256y^2-81\)
9. \(-169p^2+4\)
10. \(225a^2-16\)
11. \(25p^{8}+80p^4x+64x^2\)
12. \(100q^2-1\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(256b^{10}+160b^5p+25p^2=(16b^5+5p)^2\)
2. \(1-64b^{4}=(1-8b^2)(1+8b^2)\)
3. \(49a^{4}-25s^2=(7a^2+5s)(7a^2-5s)\)
4. \(4y^2-25b^{14}=(2y-5b^7)(2y+5b^7)\)
5. \(y^2+30y+225=(y+15)^2\)
6. \(144a^{8}-264a^4b+121b^2=(12a^4-11b)^2\)
7. \(81y^{10}-4=(9y^5+2)(9y^5-2)\)
8. \(256y^2-81=(16y+9)(16y-9)\)
9. \(-169p^2+4=(2-13p)(2+13p)\)
10. \(225a^2-16=(15a+4)(15a-4)\)
11. \(25p^{8}+80p^4x+64x^2=(5p^4+8x)^2\)
12. \(100q^2-1=(10q+1)(10q-1)\)