Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(x^2+14x+49\)
2. \(256q^{6}+224q^3s+49s^2\)
3. \(25-36b^{8}\)
4. \(-121q^2+100\)
5. \(169-4q^{12}\)
6. \(b^2-1\)
7. \(256b^{10}+32b^5+1\)
8. \(49b^{6}-225\)
9. \(225y^2-196b^{4}\)
10. \(225q^2-196\)
11. \(81s^{6}+72s^3+16\)
12. \(256p^{10}-160p^5x+25x^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(x^2+14x+49=(x+7)^2\)
2. \(256q^{6}+224q^3s+49s^2=(16q^3+7s)^2\)
3. \(25-36b^{8}=(5-6b^4)(5+6b^4)\)
4. \(-121q^2+100=(10-11q)(10+11q)\)
5. \(169-4q^{12}=(13-2q^6)(13+2q^6)\)
6. \(b^2-1=(b-1)(b+1)\)
7. \(256b^{10}+32b^5+1=(16b^5+1)^2\)
8. \(49b^{6}-225=(7b^3+15)(7b^3-15)\)
9. \(225y^2-196b^{4}=(15y-14b^2)(15y+14b^2)\)
10. \(225q^2-196=(15q+14)(15q-14)\)
11. \(81s^{6}+72s^3+16=(9s^3+4)^2\)
12. \(256p^{10}-160p^5x+25x^2=(16p^5-5x)^2\)