Question

Express each of the following as a sum of perfect squares a² + 25b²+4- 5ab - 10b -2a​

Answer 1

Multiply and divide by 2

=> 1/2 ( 2a² + 50b² + 8 - 10ab - 20b - 4a )

=> 1/2 ( a² + 25b² - 10ab + 25b² + 4 - 20b + a² + 4 - 4a )

=> 1/2 { ( a - 5b )² + ( 5b - 2 )² + ( a - 2 )² }

Hope you find it helpful.

Answer 2

Step-by-step explanation:

Factorization when the given expression is a perfect square:

(i) x4 - 10x2y2 + 25y4

Solution:

We can express the given expression x4 - 10x2y2 + 25y4 as a2 - 2ab + b2

= (x2)2 - 2 (x2) (5y2) + (5y2)2

Now it’s in the form of the formula of a2 + 2ab + b2 = (a + b)2 then we get,

= (x2 - 5y2)2

= (x2 – 5y2) (x2 – 5y2)