Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(9p^{4}-30p^2s+25s^2\)
2. \(121q^{4}-81x^2\)
3. \(9-64s^{8}\)
4. \(16b^{6}+24b^3q+9q^2\)
5. \(100a^{4}-9b^2\)
6. \(100s^{6}-180s^3y+81y^2\)
7. \(64p^{8}+176p^4+121\)
8. \(9x^{10}+30x^5+25\)
9. \(121-144p^{4}\)
10. \(144x^2+120x+25\)
11. \(9p^{6}+12p^3x+4x^2\)
12. \(4s^2-p^{4}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(9p^{4}-30p^2s+25s^2=(3p^2-5s)^2\)
2. \(121q^{4}-81x^2=(11q^2+9x)(11q^2-9x)\)
3. \(9-64s^{8}=(3-8s^4)(3+8s^4)\)
4. \(16b^{6}+24b^3q+9q^2=(4b^3+3q)^2\)
5. \(100a^{4}-9b^2=(10a^2+3b)(10a^2-3b)\)
6. \(100s^{6}-180s^3y+81y^2=(10s^3-9y)^2\)
7. \(64p^{8}+176p^4+121=(8p^4+11)^2\)
8. \(9x^{10}+30x^5+25=(3x^5+5)^2\)
9. \(121-144p^{4}=(11-12p^2)(11+12p^2)\)
10. \(144x^2+120x+25=(12x+5)^2\)
11. \(9p^{6}+12p^3x+4x^2=(3p^3+2x)^2\)
12. \(4s^2-p^{4}=(2s-p^2)(2s+p^2)\)