Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25p^2-90p+81\)
2. \(49q^{10}-126q^5+81\)
3. \(s^2+10s+25\)
4. \(b^2-4b+4\)
5. \(-81x^2+16\)
6. \(256a^{4}-160a^2x+25x^2\)
7. \(a^2-10a+25\)
8. \(256a^{6}-288a^3+81\)
9. \(a^2+26a+169\)
10. \(x^2-30x+225\)
11. \(225q^2-420q+196\)
12. \(x^2+8x+16\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25p^2-90p+81=(5p-9)^2\)
2. \(49q^{10}-126q^5+81=(7q^5-9)^2\)
3. \(s^2+10s+25=(s+5)^2\)
4. \(b^2-4b+4=(b-2)^2\)
5. \(-81x^2+16=(4-9x)(4+9x)\)
6. \(256a^{4}-160a^2x+25x^2=(16a^2-5x)^2\)
7. \(a^2-10a+25=(a-5)^2\)
8. \(256a^{6}-288a^3+81=(16a^3-9)^2\)
9. \(a^2+26a+169=(a+13)^2\)
10. \(x^2-30x+225=(x-15)^2\)
11. \(225q^2-420q+196=(15q-14)^2\)
12. \(x^2+8x+16=(x+4)^2\)