How do you use the difference of two squares formula to factor #9/x^6 - 64y^2#?

Question

Savannah Anderson · Accepted Answer

#(3/x^3-8y)(3/x^6+8y)# Using the formula #(a-b)(a+b)=a^2-b^2# we get #(3/x^3-8y)(3/x^4+8y)#

Eli Assouline · Answer

#(3/x^3-8y)(3/x^3+8y)# #•color(white)(x)a^2-b^2=(a-b)(a+b)larrcolor(blue)"difference of squares"# #9/x^6=(3/x^3)^2rArra=3/x^3# #64y^2=(8y)^2rArrb=8y# #9/x^6-64y^2=(3/x^3-8y)(3/x^3+8y)#

Abigail Allen · Answer

undefined To use the difference of two squares formula to factor $ \frac{9}{x^6} - 64y^2 $, first, express it as the difference of two squares:

$ \frac{9}{x^6} - 64y^2 = \left(\frac{3}{x^3}\right)^2 - (8y)^2 $

Now, apply the difference of two squares formula, which states that $ a^2 - b^2 = (a + b)(a - b) $:

$ \left(\frac{3}{x^3}\right)^2 - (8y)^2 = \left(\frac{3}{x^3} + 8y\right)\left(\frac{3}{x^3} - 8y\right) $

So, using the difference of two squares formula, $ \frac{9}{x^6} - 64y^2 $ factors into $ \left(\frac{3}{x^3} + 8y\right)\left(\frac{3}{x^3} - 8y\right) $.