Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(256s^2+224s+49\)
2. \(25a^{12}-1\)
3. \(16x^2-49\)
4. \(p^2-196\)
5. \(100a^{4}-180a^2p+81p^2\)
6. \(9s^{8}-48s^4x+64x^2\)
7. \(169q^2-64p^{6}\)
8. \(121b^2-286b+169\)
9. \(b^2-4b+4\)
10. \(49p^{4}+56p^2+16\)
11. \(100q^{10}+60q^5x+9x^2\)
12. \(y^2-2y+1\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(256s^2+224s+49=(16s+7)^2\)
2. \(25a^{12}-1=(5a^6+1)(5a^6-1)\)
3. \(16x^2-49=(4x+7)(4x-7)\)
4. \(p^2-196=(p+14)(p-14)\)
5. \(100a^{4}-180a^2p+81p^2=(10a^2-9p)^2\)
6. \(9s^{8}-48s^4x+64x^2=(3s^4-8x)^2\)
7. \(169q^2-64p^{6}=(13q-8p^3)(13q+8p^3)\)
8. \(121b^2-286b+169=(11b-13)^2\)
9. \(b^2-4b+4=(b-2)^2\)
10. \(49p^{4}+56p^2+16=(7p^2+4)^2\)
11. \(100q^{10}+60q^5x+9x^2=(10q^5+3x)^2\)
12. \(y^2-2y+1=(y-1)^2\)