Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100b^{14}-49q^2\)
2. \(q^2-49\)
3. \(196b^{4}+28b^2+1\)
4. \(144y^2-121q^{4}\)
5. \(256x^2-121\)
6. \(225p^{6}+30p^3+1\)
7. \(121s^{4}+44s^2+4\)
8. \(169p^{10}-100\)
9. \(256x^{6}-480x^3+225\)
10. \(x^2-16x+64\)
11. \(49a^{8}+28a^4b+4b^2\)
12. \(b^2-16\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100b^{14}-49q^2=(10b^7+7q)(10b^7-7q)\)
2. \(q^2-49=(q-7)(q+7)\)
3. \(196b^{4}+28b^2+1=(14b^2+1)^2\)
4. \(144y^2-121q^{4}=(12y-11q^2)(12y+11q^2)\)
5. \(256x^2-121=(16x+11)(16x-11)\)
6. \(225p^{6}+30p^3+1=(15p^3+1)^2\)
7. \(121s^{4}+44s^2+4=(11s^2+2)^2\)
8. \(169p^{10}-100=(13p^5+10)(13p^5-10)\)
9. \(256x^{6}-480x^3+225=(16x^3-15)^2\)
10. \(x^2-16x+64=(x-8)^2\)
11. \(49a^{8}+28a^4b+4b^2=(7a^4+2b)^2\)
12. \(b^2-16=(b-4)(b+4)\)