Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(49a^{6}-140a^3+100\)
2. \(16y^2-88y+121\)
3. \(a^2-16a+64\)
4. \(x^2-24x+144\)
5. \(81x^2-100p^{4}\)
6. \(49a^{8}-42a^4b+9b^2\)
7. \(y^2-1\)
8. \(9-4p^{12}\)
9. \(121y^2-225s^{6}\)
10. \(25x^{4}-90x^2+81\)
11. \(144p^2+120p+25\)
12. \(100a^2+140a+49\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(49a^{6}-140a^3+100=(7a^3-10)^2\)
2. \(16y^2-88y+121=(4y-11)^2\)
3. \(a^2-16a+64=(a-8)^2\)
4. \(x^2-24x+144=(x-12)^2\)
5. \(81x^2-100p^{4}=(9x-10p^2)(9x+10p^2)\)
6. \(49a^{8}-42a^4b+9b^2=(7a^4-3b)^2\)
7. \(y^2-1=(y+1)(y-1)\)
8. \(9-4p^{12}=(3-2p^6)(3+2p^6)\)
9. \(121y^2-225s^{6}=(11y-15s^3)(11y+15s^3)\)
10. \(25x^{4}-90x^2+81=(5x^2-9)^2\)
11. \(144p^2+120p+25=(12p+5)^2\)
12. \(100a^2+140a+49=(10a+7)^2\)