Factorize
Algebra
Level
2
Factorize .
(2x+3)^2+(x+4)^2
(x+2)^2+(x+1)^2
(3x+4)^2+(x+1)^2
(3x+5)^2+(x+1)^2
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Multiple choice method (the lazy method):
Just calculate how many x 2 each of the choices has
( x + 2 ) 2 + ( x + 1 ) 2 = ( x 2 + … ) + ( x 2 + … ) = 2 x 2 + … ( 2 x + 3 ) 2 + ( x + 4 ) 2 = ( 4 x 2 + … ) + ( x 2 + … ) = 5 x 2 + … ( 3 x + 4 ) 2 + ( x + 1 ) 2 = ( 9 x 2 + … ) + ( x 2 + … ) = 1 0 x 2 + … ( 3 x + 5 ) 2 + ( x + 1 ) 2 = ( 9 x 2 + … ) + ( x 2 + … ) = 1 0 x 2 + …
Pretty obvious, only ( 2 x + 3 ) 2 + ( x + 4 ) 2 satisfies the original expression.
Translation of the solution given by problem setter:
5 x 2 + 2 0 x + 2 5 = 4 x 2 + 1 2 x + 9 + x 2 + 8 x + 1 6 = ( 2 x ) 2 + 2 ( 2 x ) ( 3 ) + 3 2 + x 2 + 2 ( x ) ( 4 ) + 4 2 = ( 2 x + 3 ) 2 + ( x + 4 ) 2