Question

11. Resolve into factors: y4 + y2 + 25

Answer 1

Given : y⁴ + y² + 25

To Find :  Factorize

Solution

y⁴ + y² + 25

Add and subtract  9y²

=  y⁴ + y² + 25  + 9y²  - 9y²

=   y⁴ + 10y² +  5²  - (3y)²  

=   y⁴ + 2.y².5 +  5²  - (3y)²  

using (a + b)² = a² + 2ab + b²

a = y²  b = 5

= (y² + 5)² -  (3y)²  

using a² - b² = (a + b)(a - b)

a = y² + 5   b = 3y

=  (y² + 5 + 3y)  (y² + 5 - 3y)

=  (y²   + 3y  + 5)(y²  -3y + 5)

y⁴ + y² + 25  =  (y²   + 3y  + 5)(y²  -3y + 5)

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