Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(169a^{12}-36x^2\)
2. \(x^2-121\)
3. \(25-9q^{10}\)
4. \(169a^2-25\)
5. \(225p^2-a^{10}\)
6. \(q^2-30q+225\)
7. \(100y^{8}+140y^4+49\)
8. \(36s^{6}+60s^3y+25y^2\)
9. \(16p^{4}-24p^2s+9s^2\)
10. \(-4a^2+225\)
11. \(q^2+8q+16\)
12. \(9x^{14}-49\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(169a^{12}-36x^2=(13a^6+6x)(13a^6-6x)\)
2. \(x^2-121=(x+11)(x-11)\)
3. \(25-9q^{10}=(5-3q^5)(5+3q^5)\)
4. \(169a^2-25=(13a+5)(13a-5)\)
5. \(225p^2-a^{10}=(15p-a^5)(15p+a^5)\)
6. \(q^2-30q+225=(q-15)^2\)
7. \(100y^{8}+140y^4+49=(10y^4+7)^2\)
8. \(36s^{6}+60s^3y+25y^2=(6s^3+5y)^2\)
9. \(16p^{4}-24p^2s+9s^2=(4p^2-3s)^2\)
10. \(-4a^2+225=(15-2a)(15+2a)\)
11. \(q^2+8q+16=(q+4)^2\)
12. \(9x^{14}-49=(3x^7+7)(3x^7-7)\)