Question

Express each of the following as a sum of perfect squares a² + 25b²+4- 5ab - 10b -2a.
I want step by step explanation.​

Answer 1

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)

(ii) x2+ 6x + 9

Solution:

We can express the given expression x2 + 6x + 9 as a2 + 2ab + b2

= (x)2 + 2 (x) (3) + (3)2

Now we will apply the formula of a2 + 2ab + b2 = (a + b)2 then we get,

= (x + 3)2

= (x + 3) (x + 3)

Answer 2

hope it is helpful for you