Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100p^{4}-9y^2\)
2. \(225a^{10}-210a^5q+49q^2\)
3. \(s^2-81\)
4. \(256a^{4}-81y^2\)
5. \(a^2-81\)
6. \(144s^2+24s+1\)
7. \(121x^2-110x+25\)
8. \(q^2-2q+1\)
9. \(16b^{10}-56b^5y+49y^2\)
10. \(y^2-14y+49\)
11. \(225y^2-64p^{14}\)
12. \(25a^{4}+60a^2b+36b^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100p^{4}-9y^2=(10p^2+3y)(10p^2-3y)\)
2. \(225a^{10}-210a^5q+49q^2=(15a^5-7q)^2\)
3. \(s^2-81=(s-9)(s+9)\)
4. \(256a^{4}-81y^2=(16a^2+9y)(16a^2-9y)\)
5. \(a^2-81=(a+9)(a-9)\)
6. \(144s^2+24s+1=(12s+1)^2\)
7. \(121x^2-110x+25=(11x-5)^2\)
8. \(q^2-2q+1=(q-1)^2\)
9. \(16b^{10}-56b^5y+49y^2=(4b^5-7y)^2\)
10. \(y^2-14y+49=(y-7)^2\)
11. \(225y^2-64p^{14}=(15y-8p^7)(15y+8p^7)\)
12. \(25a^{4}+60a^2b+36b^2=(5a^2+6b)^2\)