Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(256q^2-288q+81\)
2. \(a^2-24a+144\)
3. \(25-169a^{16}\)
4. \(100a^2-60a+9\)
5. \(25b^{10}-90b^5x+81x^2\)
6. \(196p^2-252p+81\)
7. \(25s^{8}-40s^4y+16y^2\)
8. \(b^2+6b+9\)
9. \(196y^{6}-252y^3+81\)
10. \(9q^2-84q+196\)
11. \(225q^{8}+210q^4+49\)
12. \(25b^{12}-64q^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(256q^2-288q+81=(16q-9)^2\)
2. \(a^2-24a+144=(a-12)^2\)
3. \(25-169a^{16}=(5-13a^8)(5+13a^8)\)
4. \(100a^2-60a+9=(10a-3)^2\)
5. \(25b^{10}-90b^5x+81x^2=(5b^5-9x)^2\)
6. \(196p^2-252p+81=(14p-9)^2\)
7. \(25s^{8}-40s^4y+16y^2=(5s^4-4y)^2\)
8. \(b^2+6b+9=(b+3)^2\)
9. \(196y^{6}-252y^3+81=(14y^3-9)^2\)
10. \(9q^2-84q+196=(3q-14)^2\)
11. \(225q^{8}+210q^4+49=(15q^4+7)^2\)
12. \(25b^{12}-64q^2=(5b^6+8q)(5b^6-8q)\)