Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(121p^2+264p+144\)
2. \(100b^{10}-60b^5p+9p^2\)
3. \(25q^2-40q+16\)
4. \(100a^{8}+140a^4s+49s^2\)
5. \(-9y^2+169\)
6. \(9s^{4}-84s^2+196\)
7. \(9y^{12}-16\)
8. \(169p^2-225\)
9. \(16s^2+8s+1\)
10. \(36b^{4}-132b^2q+121q^2\)
11. \(-64p^2+49\)
12. \(q^2+2q+1\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(121p^2+264p+144=(11p+12)^2\)
2. \(100b^{10}-60b^5p+9p^2=(10b^5-3p)^2\)
3. \(25q^2-40q+16=(5q-4)^2\)
4. \(100a^{8}+140a^4s+49s^2=(10a^4+7s)^2\)
5. \(-9y^2+169=(13-3y)(13+3y)\)
6. \(9s^{4}-84s^2+196=(3s^2-14)^2\)
7. \(9y^{12}-16=(3y^6+4)(3y^6-4)\)
8. \(169p^2-225=(13p+15)(13p-15)\)
9. \(16s^2+8s+1=(4s+1)^2\)
10. \(36b^{4}-132b^2q+121q^2=(6b^2-11q)^2\)
11. \(-64p^2+49=(7-8p)(7+8p)\)
12. \(q^2+2q+1=(q+1)^2\)