Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(121a^2-220a+100\)
2. \(169p^{8}-312p^4x+144x^2\)
3. \(-100p^2+169\)
4. \(-225b^2+169\)
5. \(9x^2-1\)
6. \(100a^2+180a+81\)
7. \(49x^2+14x+1\)
8. \(y^2-196\)
9. \(16x^2-81\)
10. \(225y^2-1\)
11. \(p^2-121\)
12. \(81x^{6}-169\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(121a^2-220a+100=(11a-10)^2\)
2. \(169p^{8}-312p^4x+144x^2=(13p^4-12x)^2\)
3. \(-100p^2+169=(13-10p)(13+10p)\)
4. \(-225b^2+169=(13-15b)(13+15b)\)
5. \(9x^2-1=(3x+1)(3x-1)\)
6. \(100a^2+180a+81=(10a+9)^2\)
7. \(49x^2+14x+1=(7x+1)^2\)
8. \(y^2-196=(y+14)(y-14)\)
9. \(16x^2-81=(4x+9)(4x-9)\)
10. \(225y^2-1=(15y+1)(15y-1)\)
11. \(p^2-121=(p+11)(p-11)\)
12. \(81x^{6}-169=(9x^3+13)(9x^3-13)\)