Question

x^4- 10x^2y^2+25y^4
(Factorise)

Answer 1

x^4- 10x^2y^2+25y^4

= (x^2)^2- 2 (x^2) (5 y^2)+ (5y^2)^2

= (x^2-5y^2)^2

= (x^2-5y^2) (x^2-5y^2) (Answer)

Answer 2

Answer:

by factorization    $x^4 - 10x^2y^2+25y^4$  =   (x² - 5y²)(x² - 5y²)

Step-by-step explanation:

we have to factorize the equation

$x^4 - 10x^2y^2+25y^4$

it can also be represented as:

(x²)² - 10(x²)(y²) + (5y²)²

(x²)² - (2)(5)(x²)(y²) + (5y²)²

(x²)² - 2(x²)(5y²) + (5y²)²

the above equation is in form of (a² - 2ab + b²)

where 'a' and 'b' can be any numbers

substitute values

a = x² , b = 5y²

also (a² - 2ab + b²) = (a - b)²

so [(x²)² - 2(x²)(5y²) + (5y²)²]  = (x² - 5y²)²

= (x² - 5y²)(x² - 5y²)

by factorization;

$x^4 - 10x^2y^2+25y^4$  =   (x² - 5y²)(x² - 5y²)