Övn 2.1
Sommarmatte 1
(Skillnad mellan versioner)
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| - | __NOTOC__ | ||
| - | ==Övning 2.1:1== | ||
| - | <div class="ovning"> | ||
| - | Utveckla | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="33%">3x(x-1)</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="33%">(1+x-x^2)xy</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="33%">-x^2(4-y^2)</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="33%">x^3y^2\left(\displaystyle \frac{1}{y} - \frac{1}{xy}+1\right)</td> | ||
| - | <td class="ntext">e) </td> | ||
| - | <td class="ntext" width="33%">(x-7)^2</td> | ||
| - | <td class="ntext">f)</td> | ||
| - | <td class="ntext" width="33%">(5+4y)^2</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">g)</td> | ||
| - | <td class="ntext" width="33%">(y^2-3x^3)^2</td> | ||
| - | <td class="ntext">h)</td> | ||
| - | <td class="ntext" width="33%">(5x^3+3x^5)^2</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | ==Övning 2.1:2== | ||
| - | <div class="ovning"> | ||
| - | Utveckla och förenkla så långt som möjligt | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="50%">(x-4)(x-5)-3x(2x-3)</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="50%">(1-5x)(1+15x)-3(2-5x)(2+5x)</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="50%">(3x+4)^2-(3x-2)(3x-8)</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="50%">(3x^2+2)(3x^2-2)(9x^4+4)</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">e)</td> | ||
| - | <td class="ntext" width="50%">(a+b)^2+(a-b)^2</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.1:3== | ||
| - | |||
| - | <div class="ovning"> | ||
| - | Faktorisera så långt som möjligt | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="33%">x^2-36</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="33%">5x^2-20</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="33%">x^2+6x+9</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="33%">x^2-10x+25</td> | ||
| - | <td class="ntext">e)</td> | ||
| - | <td class="ntext" width="33%">18x-2x^3</td> | ||
| - | <td class="ntext">f)</td> | ||
| - | <td class="ntext" width="33%">16x^2+8x+1</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.1:4== | ||
| - | <div class="ovning"> | ||
| - | Bestäm koefficienterna framför \,x\, och \,x^2\, när följande uttryck utvecklas | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="100%">(x+2)(3x^2-x+5)</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="100%">(1+x+x^2+x^3)(2-x+x^2+x^4)</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="100%">(x-x^3+x^5)(1+3x+5x^2)(2-7x^2-x^4)</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.1:5== | ||
| - | <div class="ovning"> | ||
| - | Förenkla så långt som möjligt | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="50%">\displaystyle \frac{1}{x-x^2}-\displaystyle \frac{1}{x}</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="50%">\displaystyle \frac{1}{y^2-2y}-\displaystyle \frac{2}{y^2-4}</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="50%">\displaystyle \frac{(3x^2-12)(x^2-1)}{(x+1)(x+2)}</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="50%">\displaystyle \frac{(y^2+4y+4)(2y-4)}{(y^2+4)(y^2-4)}</td> | ||
| - | </tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.1:6== | ||
| - | <div class="ovning"> | ||
| - | Förenkla så långt som möjligt | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="50%">\left(x-y+\displaystyle\frac{x^2}{y-x}\right) \left(\displaystyle\frac{y}{2x-y}-1\right)</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="50%">\displaystyle \frac{x}{x-2}+\displaystyle \frac{x}{x+3}-2</td> | ||
| - | </tr> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="50%">\displaystyle \frac{2a+b}{a^2-ab}-\frac{2}{a-b}</td> | ||
| - | <td class="ntext">d)</td> | ||
| - | <td class="ntext" width="50%">\displaystyle\frac{a-b+\displaystyle\frac{b^2}{a+b}}{1-\left(\displaystyle\frac{a-b}{a+b}\right)^2}</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.1:7== | ||
| - | <div class="ovning"> | ||
| - | Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr align="left"> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="33%">\displaystyle \frac{2}{x+3}-\frac{2}{x+5}</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="33%">x+\displaystyle \frac{1}{x-1}+\displaystyle \frac{1}{x^2}</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="33%">\displaystyle \frac{ax}{a+1}-\displaystyle \frac{ax^2}{(a+1)^2}</td> | ||
| - | </tr> | ||
| - | </table> | ||
| - | </div> | ||
| - | |||
| - | ==Övning 2.1:8== | ||
| - | |||
| - | <div class="ovning"> | ||
| - | Förenkla följande bråkuttryck genom att skriva på gemensamt bråkstreck | ||
| - | <table width="100%" cellspacing="10px"> | ||
| - | <tr> | ||
| - | <td class="ntext">a)</td> | ||
| - | <td class="ntext" width="33%">\displaystyle \frac{\displaystyle\ \frac{x}{x+1}\ }{\ 3+x\ }</td> | ||
| - | <td class="ntext">b)</td> | ||
| - | <td class="ntext" width="33%">\displaystyle \frac{\displaystyle \frac{3}{x}-\displaystyle \frac{1}{x}}{\displaystyle \frac{1}{x-3}}</td> | ||
| - | <td class="ntext">c)</td> | ||
| - | <td class="ntext" width="33%">\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+\displaystyle \frac{1}{1+x}}}</td> | ||
| - | </tr> | ||
| - | <tr><td height="5px"/></tr> | ||
| - | </table> | ||
| - | </div> | ||
