User:Twentysand: Difference between revisions
Appearance
Content deleted Content added
No edit summary |
No edit summary |
||
Line 3: | Line 3: | ||
<math>(a^2 + b^2)^3 \ne a^6 + b^6</math> |
<math>(a^2 + b^2)^3 \ne a^6 + b^6</math> |
||
<br /><br /> |
<br /><br /> |
||
To see why, lets expand the outer exponent:<br /> |
To see why, lets expand the outer exponent:<br /> |
||
<math>(a^2 + b^2)^3 = (a^2 + b^2) \times (a^2 + b^2) \times (a^2 + b^2)</math> |
<math>(a^2 + b^2)^3 = (a^2 + b^2) \times (a^2 + b^2) \times (a^2 + b^2)</math> |
||
<br /><br /> |
<br /><br /> |
||
Actually lets do this |
Actually lets do this - since we know we can use the FOIL method to Distribute a square of sums:<br /> |
||
<math>(a^2 + b^2)^3 = (a^2 + b^2)^2 \times (a^2 + b^2)</math> |
<math>(a^2 + b^2)^3 = (a^2 + b^2)^2 \times (a^2 + b^2)</math> |
||
<br /><br /> |
<br /><br /> |
||
We can now FOIL the first part: |
We can now FOIL the first part: |
||
<br /> |
<br /> |
||
<math>(a^2 + b^2)^2 = a^4 + (a^2)(b^2) + (a^2)(b^2) + b^4</math> |
<math>(a^2 + b^2)^2 = a^4 + (a^2)(b^2) + (a^2)(b^2) + b^4</math> |
||
<br /><br /> |
<br /><br /> |
||
So now we have |
|||
<math>(a^2 + b^2)^3 = (a^4 + (a^2)(b^2) + (a^2)(b^2) + b^4) \times (a^2 + b^2)</math> |
|||
<br /><br /><br /><br /> |
|||
<math>= (a^4 + 2a^2b^2 + b^4) \times (a^2 + b^2)</math> |
<math>= (a^4 + 2a^2b^2 + b^4) \times (a^2 + b^2)</math> |
||
<br /> |
<br /> |
Revision as of 22:23, 29 October 2008
A common mistake when learning about exponents:
To see why, lets expand the outer exponent:
Actually lets do this - since we know we can use the FOIL method to Distribute a square of sums:
We can now FOIL the first part:
So now we have Failed to parse (Conversion error. Server ("https://wikimedia.org/enwiki/api/rest_") reported: "Cannot get mml. upstream connect error or disconnect/reset before headers. reset reason: connection termination"): {\displaystyle (a^{2}+b^{2})^{3}=(a^{4}+(a^{2})(b^{2})+(a^{2})(b^{2})+b^{4})\times (a^{2}+b^{2})}