Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(81b^{4}-234b^2x+169x^2\)
2. \(49q^{4}-140q^2s+100s^2\)
3. \(s^2-169\)
4. \(169y^2-81x^{12}\)
5. \(196p^2+364p+169\)
6. \(p^2-4\)
7. \(25q^2-40q+16\)
8. \(100b^{8}+220b^4p+121p^2\)
9. \(16p^{4}+40p^2+25\)
10. \(b^2-10b+25\)
11. \(y^2+24y+144\)
12. \(4x^{10}+44x^5+121\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(81b^{4}-234b^2x+169x^2=(9b^2-13x)^2\)
2. \(49q^{4}-140q^2s+100s^2=(7q^2-10s)^2\)
3. \(s^2-169=(s+13)(s-13)\)
4. \(169y^2-81x^{12}=(13y-9x^6)(13y+9x^6)\)
5. \(196p^2+364p+169=(14p+13)^2\)
6. \(p^2-4=(p+2)(p-2)\)
7. \(25q^2-40q+16=(5q-4)^2\)
8. \(100b^{8}+220b^4p+121p^2=(10b^4+11p)^2\)
9. \(16p^{4}+40p^2+25=(4p^2+5)^2\)
10. \(b^2-10b+25=(b-5)^2\)
11. \(y^2+24y+144=(y+12)^2\)
12. \(4x^{10}+44x^5+121=(2x^5+11)^2\)