Is the following expression true or false? show your work. [x^2 + 8x + 16] · [x^2 – 8x + 16] = (x^2 – 16)^2

True

Solution:

Rearrange the equation to the LHS:

[x^2 + 8x + 16] · [x^2 – 8x + 16] - (x^2 – 16)^2 = 0

Factoring  x^2+8x+16

x^2 - 4x - 4x - 16

= (x-4)  •  (x-4)

= = (x+4)2

So now we have an equation

(x + 4)^2 • (x - 4)^2 -  (x^2 - 16)^2  = 0

Step 2: Evaluate the following:

(x+4)2   =    x^2+8x+16

(x-4)2   =    x^2-8x+16  

(x^2-16)2   =    x^4-32x^2+256

(x^2+8x+16)  (x^2-8x+16  ) -  (x^4-32x^2+256 )

0 = 0

Hence True