Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(16a^{10}-56a^5+49\)
2. \(49p^2-1\)
3. \(4a^{4}+20a^2+25\)
4. \(36y^{16}-121\)
5. \(64q^2-1\)
6. \(25x^2+160x+256\)
7. \(x^2-16x+64\)
8. \(9x^{4}+96x^2+256\)
9. \(144b^{10}+24b^5q+1q^2\)
10. \(100y^2-49b^{16}\)
11. \(9-4a^{6}\)
12. \(196a^{4}-9x^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(16a^{10}-56a^5+49=(4a^5-7)^2\)
2. \(49p^2-1=(7p+1)(7p-1)\)
3. \(4a^{4}+20a^2+25=(2a^2+5)^2\)
4. \(36y^{16}-121=(6y^8+11)(6y^8-11)\)
5. \(64q^2-1=(8q+1)(8q-1)\)
6. \(25x^2+160x+256=(5x+16)^2\)
7. \(x^2-16x+64=(x-8)^2\)
8. \(9x^{4}+96x^2+256=(3x^2+16)^2\)
9. \(144b^{10}+24b^5q+1q^2=(12b^5+q)^2\)
10. \(100y^2-49b^{16}=(10y-7b^8)(10y+7b^8)\)
11. \(9-4a^{6}=(3-2a^3)(3+2a^3)\)
12. \(196a^{4}-9x^2=(14a^2+3x)(14a^2-3x)\)