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4x4 - 21 x2y2 + y4
= (4x4 + 4x2y2 + y4) - 25x2y2
= [(2x2)2 + 2x2 . 2 . y2 + (y2)2] - 25x2y2
= (2x2 + y2) - 25x2y2
= (2x2 + y2 - 5xy) (2x2 + y2 + 5xy)
a) \(x^2+4y^2+4xy\)
\(=x^2+2.x.2y+\left(2y\right)^2\)
\(=\left(x+2y\right)^2\)
b) \(\left(x+y\right)^2-\left(x-y\right)^2\)
\(=\left(x+y-x+y\right)\left(x+y+x-y\right)\)
\(=2y.2x\)
\(=4xy\)
c) \(\left(3x+1\right)^2-\left(x+1\right)^2\)
\(=\left(3x+1-x-1\right)\left(3x+1+x-1\right)\)
a) \(x^6-y^6=\left(x^2\right)^3-\left(y^2\right)^3\)
\(=\left(x^2-y^2\right)\left(x^4+x^2y^2+y^4\right)\)
\(45x\left(y-8\right)-27x\left(8-y\right)\\ =45x\left(y-8\right)+27x\left(y-8\right)\\ =\left(45x+27x\right)\left(y-8\right)\\ =72x\left(y-8\right)\)
Lời giải:
a. $45x(y-8)-27x(8-y)=45x(y-8)+27x(y-8)$
$=(45x+27x)(y-8)=72x(y-8)$
b. $x^2-49+4y^2-4xy$
$=(x^2-4xy+4y^2)-49$
$=(x-2y)^2-7^2=(x-2y-7)(x-2y+7)$
\((4x-y)(a+b)(4x-y)(c-1)\)
\(=\left(4x-y\right)\left(4x-y\right)=\left(4x-y\right)^{1+1}=\left(4y-2\right)^2\)
\(=\left(a+b\right)\left(4x-y\right)^2\left(c-1\right)\)
(4x-y)(a+b)(4x-y)(c-1)
= ( 4x - y ) ( 4x - y ) = ( 4x - y ) 1 + 1 = ( 4y - 2 ) 2
= (a + b ) ( 4x - y )2 ( c - 1 )
Ta có
a, x2-x-y2-y
=x2-y2-(x+y)
=(x-y)(x+y) - (x+y)
=(x+y)(x-y-1)
b, x2-2xy+y2-z2
=(x-y)2-z2
=(x-y-z)(x-y+z)
\(x^2-4x+4-y^2\)
\(=\left(x-2\right)^2-y^2\)
\(=\left(x-2-y\right)\left(x-2+y\right)\)