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> | ||
