Jump to content

User:Twentysand: Difference between revisions

From Wikipedia, the free encyclopedia
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 instead since we know we can use the FOIL method to Distribute a square over sums:<br />
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})}