Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(16b^2+120b+225\)
2. \(36q^{8}+132q^4+121\)
3. \(49s^2-84s+36\)
4. \(64p^{16}-9x^2\)
5. \(144q^{8}-168q^4y+49y^2\)
6. \(q^2+28q+196\)
7. \(p^2+16p+64\)
8. \(144y^2-121b^{16}\)
9. \(a^2+24a+144\)
10. \(-36q^2+121\)
11. \(169b^{10}-390b^5y+225y^2\)
12. \(x^2-100\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(16b^2+120b+225=(4b+15)^2\)
2. \(36q^{8}+132q^4+121=(6q^4+11)^2\)
3. \(49s^2-84s+36=(7s-6)^2\)
4. \(64p^{16}-9x^2=(8p^8+3x)(8p^8-3x)\)
5. \(144q^{8}-168q^4y+49y^2=(12q^4-7y)^2\)
6. \(q^2+28q+196=(q+14)^2\)
7. \(p^2+16p+64=(p+8)^2\)
8. \(144y^2-121b^{16}=(12y-11b^8)(12y+11b^8)\)
9. \(a^2+24a+144=(a+12)^2\)
10. \(-36q^2+121=(11-6q)(11+6q)\)
11. \(169b^{10}-390b^5y+225y^2=(13b^5-15y)^2\)
12. \(x^2-100=(x-10)(x+10)\)