Question

Factorise P^4+2p^2q^2+q4 by using identities

Answer 1

Application of Algebraic

Answer: On factorizing given polynomial we get of  (p² + q²) ( p² + q²).

Explanation:

Need to factorize following polynomial using algebraic identity

$p^{4} +2p^{2} q^{2} +q^{4}$

On modifying given polynomial we get

$(p^{2} )^{2} + 2p^{2} q^{2} +(q^{2} )^{2}$

using algebraic identity a²+2ab+b² = (a + b)² we get

$(p^{2} )^{2} + 2p^{2} q^{2} +(q^{2} )^{2} = (p^{2} +q^{2} )^{2}$  

=> $(p^{2} )^{2} + 2p^{2} q^{2} +(q^{2} )^{2} = (p^{2} +q^{2} ) (p^{2} +q^{2} )$

Hence on factorizing $p^{4} +2p^{2} q^{2} +q^{4}$ using algebraic identity a²+2ab+b² = (a + b)² we get (p² + q²) ( p² + q²).

#answerwithquality

#BAL