Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100a^{14}-169y^2\)
2. \(x^2-25\)
3. \(a^2-10a+25\)
4. \(p^2+30p+225\)
5. \(-4x^2+1\)
6. \(25p^{8}+160p^4s+256s^2\)
7. \(169b^2-4a^{8}\)
8. \(64y^2-169q^{4}\)
9. \(b^2-24b+144\)
10. \(16b^{6}+120b^3+225\)
11. \(36s^{8}+60s^4+25\)
12. \(-16s^2+25\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100a^{14}-169y^2=(10a^7+13y)(10a^7-13y)\)
2. \(x^2-25=(x-5)(x+5)\)
3. \(a^2-10a+25=(a-5)^2\)
4. \(p^2+30p+225=(p+15)^2\)
5. \(-4x^2+1=(1-2x)(1+2x)\)
6. \(25p^{8}+160p^4s+256s^2=(5p^4+16s)^2\)
7. \(169b^2-4a^{8}=(13b-2a^4)(13b+2a^4)\)
8. \(64y^2-169q^{4}=(8y-13q^2)(8y+13q^2)\)
9. \(b^2-24b+144=(b-12)^2\)
10. \(16b^{6}+120b^3+225=(4b^3+15)^2\)
11. \(36s^{8}+60s^4+25=(6s^4+5)^2\)
12. \(-16s^2+25=(5-4s)(5+4s)\)