Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25p^2+90p+81\)
2. \(81s^{10}-72s^5+16\)
3. \(9b^{10}+78b^5q+169q^2\)
4. \(169q^{10}-16y^2\)
5. \(36p^2+12p+1\)
6. \(36s^{8}-121\)
7. \(16p^{8}-25x^2\)
8. \(p^2-121\)
9. \(64x^{14}-225y^2\)
10. \(36b^2-25\)
11. \(49y^2-9q^{10}\)
12. \(16q^{8}+40q^4+25\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25p^2+90p+81=(5p+9)^2\)
2. \(81s^{10}-72s^5+16=(9s^5-4)^2\)
3. \(9b^{10}+78b^5q+169q^2=(3b^5+13q)^2\)
4. \(169q^{10}-16y^2=(13q^5+4y)(13q^5-4y)\)
5. \(36p^2+12p+1=(6p+1)^2\)
6. \(36s^{8}-121=(6s^4+11)(6s^4-11)\)
7. \(16p^{8}-25x^2=(4p^4+5x)(4p^4-5x)\)
8. \(p^2-121=(p+11)(p-11)\)
9. \(64x^{14}-225y^2=(8x^7+15y)(8x^7-15y)\)
10. \(36b^2-25=(6b+5)(6b-5)\)
11. \(49y^2-9q^{10}=(7y-3q^5)(7y+3q^5)\)
12. \(16q^{8}+40q^4+25=(4q^4+5)^2\)