Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(4x^2-81q^{4}\)
2. \(1-144b^{16}\)
3. \(25a^{10}-140a^5x+196x^2\)
4. \(169p^{12}-64\)
5. \(169p^{6}-104p^3x+16x^2\)
6. \(100b^{8}+220b^4y+121y^2\)
7. \(36s^{8}+12s^4y+1y^2\)
8. \(81s^2-100b^{16}\)
9. \(4q^{8}+52q^4+169\)
10. \(4b^2+12b+9\)
11. \(x^2-20x+100\)
12. \(81b^{8}+90b^4p+25p^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(4x^2-81q^{4}=(2x-9q^2)(2x+9q^2)\)
2. \(1-144b^{16}=(1-12b^8)(1+12b^8)\)
3. \(25a^{10}-140a^5x+196x^2=(5a^5-14x)^2\)
4. \(169p^{12}-64=(13p^6+8)(13p^6-8)\)
5. \(169p^{6}-104p^3x+16x^2=(13p^3-4x)^2\)
6. \(100b^{8}+220b^4y+121y^2=(10b^4+11y)^2\)
7. \(36s^{8}+12s^4y+1y^2=(6s^4+y)^2\)
8. \(81s^2-100b^{16}=(9s-10b^8)(9s+10b^8)\)
9. \(4q^{8}+52q^4+169=(2q^4+13)^2\)
10. \(4b^2+12b+9=(2b+3)^2\)
11. \(x^2-20x+100=(x-10)^2\)
12. \(81b^{8}+90b^4p+25p^2=(9b^4+5p)^2\)