Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(169b^{4}-312b^2+144\)
2. \(y^2-20y+100\)
3. \(x^2+28x+196\)
4. \(9q^2-49\)
5. \(16s^2-24s+9\)
6. \(49b^{10}-9q^2\)
7. \(100q^{8}+140q^4s+49s^2\)
8. \(y^2-2y+1\)
9. \(-81x^2+169\)
10. \(25q^{6}+110q^3+121\)
11. \(x^2-121\)
12. \(9b^{16}-100\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(169b^{4}-312b^2+144=(13b^2-12)^2\)
2. \(y^2-20y+100=(y-10)^2\)
3. \(x^2+28x+196=(x+14)^2\)
4. \(9q^2-49=(3q+7)(3q-7)\)
5. \(16s^2-24s+9=(4s-3)^2\)
6. \(49b^{10}-9q^2=(7b^5+3q)(7b^5-3q)\)
7. \(100q^{8}+140q^4s+49s^2=(10q^4+7s)^2\)
8. \(y^2-2y+1=(y-1)^2\)
9. \(-81x^2+169=(13-9x)(13+9x)\)
10. \(25q^{6}+110q^3+121=(5q^3+11)^2\)
11. \(x^2-121=(x-11)(x+11)\)
12. \(9b^{16}-100=(3b^8+10)(3b^8-10)\)