Respuesta :
Answer:
see explanation
Step-by-step explanation:
Given
9[tex]x^{4}[/tex] - 225[tex]y^{8}[/tex] ← factor out 9 from each term
= 9( [tex]x^{4}[/tex] - 25[tex]y^{8}[/tex] ) ← difference of squares
Difference of squares factors in general as
a² - b² = (a - b)(a + b)
[tex]x^{4}[/tex] = (x² )² ⇒ a = x²
25[tex]y^{8}[/tex] = (5[tex]y^{4}[/tex] )² ⇒ b = 5[tex]y^{4}[/tex]
Hence
[tex]x^{4}[/tex] - 25[tex]y^{8}[/tex]
= ( [tex]x^{4}[/tex] -5[tex]y^{4}[/tex] )( [tex]x^{4}[/tex] + 5[tex]y^{4}[/tex] )
Thus
9[tex]x^{4}[/tex] - 225[tex]y^{8}[/tex]
= 9 ([tex]x^{4}[/tex] - 5[tex]y^{4}[/tex] )( [tex]x^{4}[/tex] + 5[tex]y^{4}[/tex] )
Answer:
[tex]9(x^2+5y^4)(x^2-5y^4)[/tex]
Step-by-step explanation:
[tex]9x^4 -225y^8[/tex]
Greatest common factor is 9
[tex]9x^4 -225y^8[/tex]
[tex]9(x^4 -25y^8)[/tex]
Now we write the temrs in sqaure form
[tex]9((x^2)^2-(5y^4)^2)[/tex]
Now apply a^2-b^2 formula
[tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]9((x^2)^2-(5y^4)^2)[/tex]
[tex]9(x^2+5y^4)(x^2-5y^4)[/tex]
Its completely factored
