Question 595767
16c<sup>6</sup> - 2f<sup>6</sup>
<pre>
Factor out 2:

2(8c<sup>6</sup> - f<sup>6</sup>)


Write the expression in parentheses as the difference of two
cubes.  The trickiest part is writing the first term 8c<sup>6</sup> as a cube:

8c<sup>6</sup> = 2<sup>3</sup>c<sup>6</sup> = 2<sup>3</sup>(c<sup>2</sup>)<sup>3</sup> = [2(c<sup>2</sup>)]<sup>3</sup> = [2c<sup>2</sup>]<sup>3</sup> = (2c<sup>2</sup>)<sup>3</sup>

f<sup>6</sup>) is easily written as a cube this way: (f<sup>2</sup>)<sup>3</sup>.

Change parentheses to brackets so you can have parentheses inside. 

 2[2<sup>3</sup>c<sup>2</sup>)<sup>3</sup> - (f<sup>2</sup>)<sup>3</sup>]

Rule: A³-B³ = (A-B)(A²+AB+B²)


2[(2c²) - (f²)][(2c²)² + (2c²)(f²) + (f²)²]

Sinplify

2(2c<sup>2</sup>-f<sup>2</sup>)(4c<sup>4</sup>+2c<sup>2</sup>f<sup>2</sup>+f<sup>4</sup>)


Edwin</pre>