分解因式 (x+2y)²-x²-2xy -7m(m-n)³+21mn(n-m)² (3a-4b)(7a-8b)+(11a+2b)(8b-7a)

分解因式 (x+2y)²-x²-2xy -7m(m-n)³+21mn(n-m)² (3a-4b)(7a-8b)+(11a+2b)(8b-7a)
分解因式 (x+2y)²-x²-2xy -7m(m-n)³+21mn(n-m)² (3a-4b)(7a-8b)+(11a+2b)(8b-7a)

分解因式 (x+2y)²-x²-2xy -7m(m-n)³+21mn(n-m)² (3a-4b)(7a-8b)+(11a+2b)(8b-7a)
( x + 2y )" - x" - 2xy
= ( x + 2y )" - x" - 2xy - y" + y"
= ( x + 2y )" - ( x + y )" + y"
= ( x + 2y - x - y )( x + 2y + x + y ) + y"
= y( 2x + 3y ) + y"
= y( 2x + 3y + y )
= 2y( x + 2y )
-7m( m - n )"' + 21mn( n - m )"
= 21mn( m - n )" - 7m( m - n )"'
= 7m( m - n )"( 3n - m + n )
= 7m( 4n - m )( m - n )"
( 3a - 4b )( 7a - 8b ) + ( 11a + 2b )( 8b - 7a )
= ( 3a - 4b )( 7a - 8b ) - ( 11a + 2b )( 7a - 8b )
= ( 3a - 4b - 11a - 2b )( 7a - 8b )
= ( - 8a - 6b )( 7a - 8b )
= -2( 4a + 3b )( 7a - 8b )

(x+2y)²-x²-2xy
=(x+2y)²-x(x+2y)
=(x+2y)(x+2y-x)
=2y(x+2y)
-7m(m-n)³+21mn(n-m)²
=7m(n-m)³+21mn(n-m)²
=7m(n-m)²(n-m+3n)
=7m(n-m)²...

全部展开

(x+2y)²-x²-2xy
=(x+2y)²-x(x+2y)
=(x+2y)(x+2y-x)
=2y(x+2y)
-7m(m-n)³+21mn(n-m)²
=7m(n-m)³+21mn(n-m)²
=7m(n-m)²(n-m+3n)
=7m(n-m)²(4n-m)
(3a-4b)(7a-8b)+(11a+2b)(8b-7a)
=(3a-4b)(7a-8b)-(11a+2b)(7a-8b)
=(7a-8b)(3a-4b-11a-2b)
=(7a-8b)(-8a-6b)
=-2(7a-8b)(4a+3b)

收起