Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(16b^{4}+40b^2s+25s^2\)
2. \(b^2+14b+49\)
3. \(4a^{14}-9b^2\)
4. \(49x^{14}-225\)
5. \(q^2-81\)
6. \(s^2+28s+196\)
7. \(100s^{10}+140s^5x+49x^2\)
8. \(a^2-30a+225\)
9. \(64x^2-169b^{10}\)
10. \(q^2-121\)
11. \(p^2+30p+225\)
12. \(169x^2+364x+196\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(16b^{4}+40b^2s+25s^2=(4b^2+5s)^2\)
2. \(b^2+14b+49=(b+7)^2\)
3. \(4a^{14}-9b^2=(2a^7+3b)(2a^7-3b)\)
4. \(49x^{14}-225=(7x^7+15)(7x^7-15)\)
5. \(q^2-81=(q-9)(q+9)\)
6. \(s^2+28s+196=(s+14)^2\)
7. \(100s^{10}+140s^5x+49x^2=(10s^5+7x)^2\)
8. \(a^2-30a+225=(a-15)^2\)
9. \(64x^2-169b^{10}=(8x-13b^5)(8x+13b^5)\)
10. \(q^2-121=(q-11)(q+11)\)
11. \(p^2+30p+225=(p+15)^2\)
12. \(169x^2+364x+196=(13x+14)^2\)