Question

Express as perfect square: x^4 + 2x^3 +3x^2 +2x+1​

Answer 1

Answer:

( x²+ x + 1 )²

Step-by-step explanation:

If we complete the square x^4 + 2x³ , we will get, x² as the the third term.

∴ x^4 + 2x³ + 3x² +2x +1 ,

= ( x^4+2x³+x²) + 2x²+2x+1 ,

= { ( x²)² + 2(x²)(x)+(x)²} + 2(x²+x)+1 ,

= ( x²+ x )² + 2( x²+ x ) ( 1 ) + 1²,

=( x²+ x + 1 )²

= y²+ 2y+1 , where, y = x²+x ,

= (y + 1)² .

Sub.ing y = x²+x , we find,

The Expression= ( x²+ x + 1 )².