Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25x^2+80x+64\)
2. \(25q^{4}-140q^2+196\)
3. \(81p^2+126p+49\)
4. \(256s^2-480s+225\)
5. \(196-81s^{10}\)
6. \(s^2+2s+1\)
7. \(4s^{6}+4s^3y+1y^2\)
8. \(121y^2-49b^{10}\)
9. \(100p^2-1\)
10. \(b^2-225\)
11. \(100b^{6}-60b^3p+9p^2\)
12. \(25q^2-4\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25x^2+80x+64=(5x+8)^2\)
2. \(25q^{4}-140q^2+196=(5q^2-14)^2\)
3. \(81p^2+126p+49=(9p+7)^2\)
4. \(256s^2-480s+225=(16s-15)^2\)
5. \(196-81s^{10}=(14-9s^5)(14+9s^5)\)
6. \(s^2+2s+1=(s+1)^2\)
7. \(4s^{6}+4s^3y+1y^2=(2s^3+y)^2\)
8. \(121y^2-49b^{10}=(11y-7b^5)(11y+7b^5)\)
9. \(100p^2-1=(10p+1)(10p-1)\)
10. \(b^2-225=(b+15)(b-15)\)
11. \(100b^{6}-60b^3p+9p^2=(10b^3-3p)^2\)
12. \(25q^2-4=(5q+2)(5q-2)\)