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Đặt x2 + 4x + 8 = A. Ta sẽ được:
A2 + 3xA + 2x2
= A2 - xA - 2xA + 2x2
= A(A-x) - 2x(A-x)
= (A-x)(A-2x)
= (x2+3x+8)(x2+2x+8)
a)\(7x\left(y-4\right)^2-\left(4-y\right)^3=7x\left(4-y\right)^2-\left(4-y\right)^3=\left(4-y\right)^2\left(7x-4+y\right)\)
b)\(\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9\left(8-4x\right)\)
\(=\left(4x-8\right)\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)-9\left(4x-8\right)\)
\(=\left(4x-8\right)\left(x^2-x-10\right)=4\left(x-2\right)\left(x^2-x-10\right)\)
a.\(7x.\left(y-4\right)^2-\left(4-y\right)^3\)=\(7x.\left(4-y\right)^2-\left(4-y\right)^3=\left(4-y\right)^2.\left(7x+y-4\right)\)
b.\(\left(4x-8\right).\left(x^2+6\right)-\left(4x-8\right)\left(x+7\right)+9.\left(8-4x\right)\)
=\(\left(4x-8\right)\left(x^2+6-x-7-9\right)=\left(4x-8\right)\left(x^2-x-10\right)\)
a) 4xn+2 + 8xn = 4xn( x2 + 2 )
b) ( 4x - 8 )( x2 + 6 ) - ( x - 2 )( x + 7 ) - 10 + 5x
= 4( x - 2 )( x2 + 6 ) - ( x - 2 )( x + 7 ) + 5( x - 2 )
= ( x - 2 )[ 4( x2 + 6 ) - ( x + 7 ) + 5 ]
= ( x - 2 )( 4x2 + 24 - x - 7 + 5 )
= ( x - 2 )( 4x2 - x + 22)
Ta có : 5x(x - 2y) + 2(2y - x)2
= 5x(x - 2y) + 2(x - 2y)2 (vì (2y - x)2 = (x - 2y)2 )
= (x - 2y)[5x + 2(x - 2y)]
= (x - 2y)(5x + 2x - 4y)
= (x - 2y)(7x - 4y)
b) 7x(y - 4)2 - (4 - y)3
= 7x(y - 4)2 - (4 - y)2(4 - y)
= 7x(y - 4)2 - (y - 4)2(4 - y)
= (y - 4)2(7x - 4 + y)
c) (4x - 8)(x2 + 6) - (4x - 8)(x + 7) + 9(8 - 4x)
= (4x - 8)(x2 + 6) - (4x - 8)(x + 7) - 9(4x - 8)
= (4x - 8)(x2 + 6 - x - 7 - 9)
= 2(x - 4)(x2 - x - 10)
\(\left(x+2\right)\left(x+3\right)\left(x+8\right)\left(x+12\right)-4x^2\)
\(=\left(x+2\right)\left(x+12\right)\left(x+3\right)\left(x+8\right)-4x^2\)
\(=\left(x^2+14x+24\right)\left(x^2+11x+24\right)-\left(2x\right)^2\)
Đặt \(x^2+11x+24=a\)
\(=a\left(a+3x\right)-4x^2=a^2+3ax-4x^2=a^2-ax+4ax-4x^2=\left(a-x\right)\left(a+4x\right)\)
( 4x - 8 ) . ( x2 + 6 ) - ( 4x - 8 ) . ( x + 7 ) + 9 . ( 8 - 4x )
= (4x - 8 ) . ( x2 + 6 ) - ( 4x - 8 ) . ( x + 7 ) - 9 . (4x - 8)
= (4x-8) ( x2+6 - x - 7 - 9)
= 4(x-2)(x^2 -x - 10)