Question

5y^5-405y
Kindly Factorise the above stated Equation 4 me, it's mandatory & I need it !!
Please!!

Answer 1

Required Answer:-

Given to factorise:

• 5y^5 - 405y

Solution:

$\sf {5y}^{5} - 405y$

$\sf = 5y( {y}^{4} - 81)$

$\sf = 5y( ({y}^{2})^{2} - {(9)}^{2} )$

$\sf = 5y({y}^{2}+ 9 )( {y}^{2} - 9)$

$\sf = 5y({y}^{2}+ 9 )( {(y)}^{2} - {(3)}^{2} )$

$\sf = 5y({y}^{2}+ 9 )(y + 3)(y - 3)$

Hence, the factorised form is 5y(y² + 9)(y + 3)(y - 3)

Identity Used:

• a² - b² = (a + b)(a - b)

Other Identities:

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• (a + b)² = (a - b)² + 4ab
• (a - b)² = (a + b)² - 4ab etc.