5( x + 2y )2 - ( 3y + 2x )2 + ( 4x - y )2 +3( 2y + x)(x - 2y)
= 5x2 + 20xy + 20y2 - 9y2 - 12xy - 4x2 + 16x2 - 8xy + y2 + 3x2 - 12y2
= 20x2
=> ĐPCM
d) 5( x + 2y )2 - ( 3y + 2x )2 + ( 4x - y )2 +3( 2y + x)(x - 2y) = 20x2
Ta có:
d) 5( x + 2y )2 - ( 3y + 2x )2 + ( 4x - y )2 +3( 2y + x)(x - 2y)
=5.[x2+2.x.2y+(2y)2 ] - [(3y)2+2.3y.2x+(2x)2 ] + [(4x)2 - 2.4x.y+y2 ] + 3.[x2 - (2y)2 ]
=5x2 + 20xy +20y2 - 9y2 - 12xy - 4x2 + 16x2 - 8xy + y2+3x2 - 12y2
=20x2(đpcm)
5( x + 2y )2 - ( 3y + 2x )2 + ( 4x - y )2 + 3( 2y + x )( x - 2y )
= 5( x2 + 4xy + 4y2 ) - ( 9y2 + 12xy + 4x2 ) + ( 16x2 - 8xy + y2 ) + 3( x2 - 4y2 )
= 5x2 + 20xy + 20y2 - 9y2 - 12xy - 4x2 + 16x2 - 8xy + y2 + 3x2 - 12y2
= 20x2 = VP ( đpcm )
Trả lời:
\(5.\left(x+2y\right)^2-\left(3y+2x\right)^2+\left(4x-y\right)^2+3.\left(2y+x\right).\left(x-2y\right)\)
\(=5.\left(x^2+4xy+4y^2\right)-\left(9y^2+12xy+4x^2\right)+\left(16x^2-8xy+y^2\right)+3.\left(x+2y\right).\left(x-2y\right)\)
\(=5x^2+20xy+20y^2-9y^2-12xy-4x^2+16x^2-8xy+y^2+3.\left(x^2-4y^2\right)\)
\(=5x^2+20xy+20y^2-9y^2-12xy-4x^2+16x^2-8xy+y^2+3x^2-12y^2\)
\(=20x^2\left(đpcm\right)\)
Học tốt
a, \(5\left(x+2y\right)^2-\left(3y+2x\right)^2+\left(4x-y\right)^2+3\left(2y+x\right)\left(x-2y\right)=20x^2\)
\(5x^2+20xy+20y^2-9y^2-12xy-4x^2+16x^2-8xy+y^2+3x^2-12y^2=VP\)
\(20x^2=VP\left(đpcm\right)\)
