Question

factorize ( x + 5 ) ( x + 2 ) ( x - 5 ) ( x - 2 ) + 4x²​

Answer 1

Step-by-step explanation:

$( x + 5 ) ( x + 2 ) ( x - 5 ) ( x - 2 ) + 4 {x}^{2}$

= $( {x}^{2} - 25)( {x}^{2} - 4) + 4 {x}^{2}$

= ${x}^{4} - 4 {x}^{2} - 25 {x}^{2} + 100 + 4 {x}^{2}$

= ${x}^{4} \cancel{ \: - 4 {x}^{2} } - 25 {x}^{2} + 100 \: \cancel{ + 4 {x}^{2} }$

= ${x}^{4} - 20 {x}^{2} - 5 {x}^{2} + 100$

= ${x}^{2} ( {x}^{2} - 20 ) - 5( {x}^{2} - 20)$

= $( {x}^{2} - 20)( {x}^{2} - 5)$