Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(9p^{16}-1\)
2. \(a^2+30a+225\)
3. \(225q^2+30q+1\)
4. \(169-36y^{12}\)
5. \(49s^2-140s+100\)
6. \(49p^{4}-81\)
7. \(169a^{10}-130a^5x+25x^2\)
8. \(16y^2-56y+49\)
9. \(p^2+4p+4\)
10. \(x^2-20x+100\)
11. \(25p^{6}-90p^3q+81q^2\)
12. \(49p^2+154p+121\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(9p^{16}-1=(3p^8+1)(3p^8-1)\)
2. \(a^2+30a+225=(a+15)^2\)
3. \(225q^2+30q+1=(15q+1)^2\)
4. \(169-36y^{12}=(13-6y^6)(13+6y^6)\)
5. \(49s^2-140s+100=(7s-10)^2\)
6. \(49p^{4}-81=(7p^2+9)(7p^2-9)\)
7. \(169a^{10}-130a^5x+25x^2=(13a^5-5x)^2\)
8. \(16y^2-56y+49=(4y-7)^2\)
9. \(p^2+4p+4=(p+2)^2\)
10. \(x^2-20x+100=(x-10)^2\)
11. \(25p^{6}-90p^3q+81q^2=(5p^3-9q)^2\)
12. \(49p^2+154p+121=(7p+11)^2\)