Algebra: Binomin neliö
https://peda.net/id/fa45f3720c6
2017-08-03T20:21:10+03:00
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Binomin neliö
https://peda.net/id/e09a2a820c6
2017-03-19T09:25:51+02:00
Binomilla tarkoitetaan kahden mielivaltaisen termin summaa, esimerkiksi<br/>
<br/>
a + b ja a − b.<br/>
<br/>
Tällaisen lausekkeen potenssit, erityisesti neliöt, noudattavat muistisääntöjä:<br/>
<br/>
(a + b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2<br/>
</sup>(a − b)<sup>2</sup> = a<sup>2</sup> − 2ab + b<sup>2<br/>
<br/>
</sup><b>Esim</b>.<br/>
a. (1 + x)<sup>2</sup> = 1<sup>2</sup> + 2⋅1⋅x + x<sup>2</sup> = x<sup>2</sup> + 2x + 1<br/>
b. (2y − 3)<sup>2</sup> = (2y)<sup>2</sup> − 3 ⋅ 2y + 3<sup>2</sup> = 4y<sup>2</sup> − 6y + 9<br/>
c. (z − <sup>1</sup>/<sub>2</sub>)<sup>2</sup> = z<sup>2</sup> − 2 ⋅ <sup>1</sup>/<sub>2</sub> + (<sup>1</sup>/<sub>2</sub>)<sup>2</sup> = z<sup>2</sup> − z + <sup>1</sup>/<sub>4</sub>
2017-03-19T08:11:23+02:00
Tehtävät
https://peda.net/id/0431462e0c7
2017-03-19T08:50:01+02:00
Sievennä.<br/>
<br/>
1. (2 + x)<sup>2</sup> <br/>
2. (1 + 2x)<sup>2</sup><br/>
3. (1 − 2x)<sup>2</sup><br/>
4. (3x + 2)<sup>2</sup><br/>
5. (<sup>2</sup>/<sub>3</sub>x − 9)<br/>
6. (x + √2)<sup>2</sup>
2017-03-19T08:48:10+02:00