Lösung 2.1:2b

Aus Online Mathematik Brückenkurs 1

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K
K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel))
Zeile 1: Zeile 1:
We expand the first product of bracketed terms by multiplying each term inside the first bracket by each term from the second bracket
We expand the first product of bracketed terms by multiplying each term inside the first bracket by each term from the second bracket
-
{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
(1-5x)(1+15x) &= 1\cdot 1+1\cdot 15x-5x\cdot 1-5x \cdot 15x\\
(1-5x)(1+15x) &= 1\cdot 1+1\cdot 15x-5x\cdot 1-5x \cdot 15x\\
&=1+15x-5x-75x^2\\
&=1+15x-5x-75x^2\\
Zeile 9: Zeile 9:
As for the second expression, we can use the conjugate rule <math>(a-b)(a+b)=a^2-b^2,</math> where <math>a=2</math> and <math> b=5x</math>,
As for the second expression, we can use the conjugate rule <math>(a-b)(a+b)=a^2-b^2,</math> where <math>a=2</math> and <math> b=5x</math>,
-
{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
3(2-5x)(2+5x) &= 3\big( 2^2-(5x)^2\big)\\
3(2-5x)(2+5x) &= 3\big( 2^2-(5x)^2\big)\\
&=3(4-25x^2)\\
&=3(4-25x^2)\\
Zeile 17: Zeile 17:
All together, we obtain
All together, we obtain
-
{{Displayed math||<math>\begin{align}
+
{{Abgesetzte Formel||<math>\begin{align}
(1-5x)(1+15x)-3(2-5x)(2+5x) &= (1+10x-75x^2)-(12-75x^2)\\
(1-5x)(1+15x)-3(2-5x)(2+5x) &= (1+10x-75x^2)-(12-75x^2)\\
&= 1+10x-75x^2-12+75x^2\\
&= 1+10x-75x^2-12+75x^2\\

Version vom 08:21, 22. Okt. 2008

We expand the first product of bracketed terms by multiplying each term inside the first bracket by each term from the second bracket

\displaystyle \begin{align}

(1-5x)(1+15x) &= 1\cdot 1+1\cdot 15x-5x\cdot 1-5x \cdot 15x\\ &=1+15x-5x-75x^2\\ &=1+10x-75x^2\,\textrm{.} \end{align}

As for the second expression, we can use the conjugate rule \displaystyle (a-b)(a+b)=a^2-b^2, where \displaystyle a=2 and \displaystyle b=5x,

\displaystyle \begin{align}

3(2-5x)(2+5x) &= 3\big( 2^2-(5x)^2\big)\\ &=3(4-25x^2)\\ &=12-75x^2\,\textrm{.} \end{align}

All together, we obtain

\displaystyle \begin{align}

(1-5x)(1+15x)-3(2-5x)(2+5x) &= (1+10x-75x^2)-(12-75x^2)\\ &= 1+10x-75x^2-12+75x^2\\ &= 1-12+10x-75x^2+75x^2\\ &=-11+10x\,\textrm{.} \end{align}

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_2.1:2b“