Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(y^2-14y+49\)
2. \(9a^{6}-12a^3y+4y^2\)
3. \(100p^2-1\)
4. \(a^2-2a+1\)
5. \(169-9b^{12}\)
6. \(81x^2+252x+196\)
7. \(25p^2-4a^{8}\)
8. \(169q^{8}-156q^4y+36y^2\)
9. \(169y^2+26y+1\)
10. \(16y^{10}-56y^5+49\)
11. \(16b^2-120b+225\)
12. \(q^2-4q+4\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(y^2-14y+49=(y-7)^2\)
2. \(9a^{6}-12a^3y+4y^2=(3a^3-2y)^2\)
3. \(100p^2-1=(10p+1)(10p-1)\)
4. \(a^2-2a+1=(a-1)^2\)
5. \(169-9b^{12}=(13-3b^6)(13+3b^6)\)
6. \(81x^2+252x+196=(9x+14)^2\)
7. \(25p^2-4a^{8}=(5p-2a^4)(5p+2a^4)\)
8. \(169q^{8}-156q^4y+36y^2=(13q^4-6y)^2\)
9. \(169y^2+26y+1=(13y+1)^2\)
10. \(16y^{10}-56y^5+49=(4y^5-7)^2\)
11. \(16b^2-120b+225=(4b-15)^2\)
12. \(q^2-4q+4=(q-2)^2\)