Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(a^2-64\)
2. \(25y^2-36q^{6}\)
3. \(225q^{10}+30q^5y+1y^2\)
4. \(196q^{8}+28q^4y+1y^2\)
5. \(b^2+18b+81\)
6. \(121x^2-154x+49\)
7. \(49a^{4}+210a^2b+225b^2\)
8. \(225a^{4}-121y^2\)
9. \(49s^2-225a^{12}\)
10. \(1-81y^{10}\)
11. \(q^2+10q+25\)
12. \(144q^{6}-168q^3+49\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(a^2-64=(a-8)(a+8)\)
2. \(25y^2-36q^{6}=(5y-6q^3)(5y+6q^3)\)
3. \(225q^{10}+30q^5y+1y^2=(15q^5+y)^2\)
4. \(196q^{8}+28q^4y+1y^2=(14q^4+y)^2\)
5. \(b^2+18b+81=(b+9)^2\)
6. \(121x^2-154x+49=(11x-7)^2\)
7. \(49a^{4}+210a^2b+225b^2=(7a^2+15b)^2\)
8. \(225a^{4}-121y^2=(15a^2+11y)(15a^2-11y)\)
9. \(49s^2-225a^{12}=(7s-15a^6)(7s+15a^6)\)
10. \(1-81y^{10}=(1-9y^5)(1+9y^5)\)
11. \(q^2+10q+25=(q+5)^2\)
12. \(144q^{6}-168q^3+49=(12q^3-7)^2\)