Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(169b^2-64a^{16}\)
2. \(100x^{4}-260x^2+169\)
3. \(49p^{14}-225x^2\)
4. \(y^2-49\)
5. \(64a^2-112a+49\)
6. \(144b^{8}+120b^4y+25y^2\)
7. \(4b^{4}+12b^2+9\)
8. \(256a^{12}-9s^2\)
9. \(121p^{4}+22p^2y+1y^2\)
10. \(121q^{6}-286q^3x+169x^2\)
11. \(y^2-225\)
12. \(100q^{14}-49\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(169b^2-64a^{16}=(13b-8a^8)(13b+8a^8)\)
2. \(100x^{4}-260x^2+169=(10x^2-13)^2\)
3. \(49p^{14}-225x^2=(7p^7+15x)(7p^7-15x)\)
4. \(y^2-49=(y-7)(y+7)\)
5. \(64a^2-112a+49=(8a-7)^2\)
6. \(144b^{8}+120b^4y+25y^2=(12b^4+5y)^2\)
7. \(4b^{4}+12b^2+9=(2b^2+3)^2\)
8. \(256a^{12}-9s^2=(16a^6+3s)(16a^6-3s)\)
9. \(121p^{4}+22p^2y+1y^2=(11p^2+y)^2\)
10. \(121q^{6}-286q^3x+169x^2=(11q^3-13x)^2\)
11. \(y^2-225=(y-15)(y+15)\)
12. \(100q^{14}-49=(10q^7+7)(10q^7-7)\)