Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(4b^{10}+20b^5x+25x^2\)
2. \(y^2-121\)
3. \(-4p^2+9\)
4. \(49x^{10}+210x^5+225\)
5. \(169q^{6}+390q^3+225\)
6. \(25a^{16}-4x^2\)
7. \(9a^2+24a+16\)
8. \(4-25p^{4}\)
9. \(100a^{10}-260a^5+169\)
10. \(100y^{10}-60y^5+9\)
11. \(p^2-6p+9\)
12. \(16s^2+40s+25\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(4b^{10}+20b^5x+25x^2=(2b^5+5x)^2\)
2. \(y^2-121=(y-11)(y+11)\)
3. \(-4p^2+9=(3-2p)(3+2p)\)
4. \(49x^{10}+210x^5+225=(7x^5+15)^2\)
5. \(169q^{6}+390q^3+225=(13q^3+15)^2\)
6. \(25a^{16}-4x^2=(5a^8+2x)(5a^8-2x)\)
7. \(9a^2+24a+16=(3a+4)^2\)
8. \(4-25p^{4}=(2-5p^2)(2+5p^2)\)
9. \(100a^{10}-260a^5+169=(10a^5-13)^2\)
10. \(100y^{10}-60y^5+9=(10y^5-3)^2\)
11. \(p^2-6p+9=(p-3)^2\)
12. \(16s^2+40s+25=(4s+5)^2\)