Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(-16b^2+9\)
2. \(81a^{6}-72a^3s+16s^2\)
3. \(16a^{4}-120a^2q+225q^2\)
4. \(64b^{4}-112b^2+49\)
5. \(64p^{10}+48p^5x+9x^2\)
6. \(49y^{4}-28y^2+4\)
7. \(-9b^2+100\)
8. \(y^2-26y+169\)
9. \(25q^{12}-121\)
10. \(16b^{4}-121\)
11. \(81q^2-16p^{8}\)
12. \(q^2+6q+9\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(-16b^2+9=(3-4b)(3+4b)\)
2. \(81a^{6}-72a^3s+16s^2=(9a^3-4s)^2\)
3. \(16a^{4}-120a^2q+225q^2=(4a^2-15q)^2\)
4. \(64b^{4}-112b^2+49=(8b^2-7)^2\)
5. \(64p^{10}+48p^5x+9x^2=(8p^5+3x)^2\)
6. \(49y^{4}-28y^2+4=(7y^2-2)^2\)
7. \(-9b^2+100=(10-3b)(10+3b)\)
8. \(y^2-26y+169=(y-13)^2\)
9. \(25q^{12}-121=(5q^6+11)(5q^6-11)\)
10. \(16b^{4}-121=(4b^2+11)(4b^2-11)\)
11. \(81q^2-16p^{8}=(9q-4p^4)(9q+4p^4)\)
12. \(q^2+6q+9=(q+3)^2\)