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\(16x^2+y^2+4y-16x-8xy\)
\(=\left(4x-y\right)^2-4\left(4x-y\right)\)
\(=\left(4x-y\right)\left(4x-y-4\right)\)
a) \(16x^2+y^2+4y-16x-8xy\)
\(=\left(4x\right)^2-8xy+y^2+4\left(y-4x\right)\)
\(=\left(4x-y\right)^2+4\left(y-4x\right)\)
\(=\left(y-4x\right)^2+4\left(y-4x\right)=\left(y-4x\right)\left(y-4x+4\right)\)
\(b,2x^2+4x+2-2y^2\)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left[\left(x+1\right)^2-y^2\right]\)
\(=2\left(x+1+y\right)\left(x+1-y\right)\)
a) \(3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)\)
\(=\left(x+1\right)\left[3x\left(x+1\right)-5x^2+7\right]\)
\(=\left(x+1\right)\left(3x^2+3x-5x^2+7\right)\)
\(=\left(x+1\right)\left(-2x^2+3x+7\right)\)
\(=-\left(x+1\right)\left(2x^2-3x-7\right)\)
b) \(\left(x+y\right)\left(2x-y\right)-\left(3x-y\right)\left(y-2x\right)\)
\(=\left(x+y\right)\left(2x-y\right)+\left(3x-y\right)\left(2x-y\right)\)
\(=\left(2x-y\right)\left(x+y+3x-y\right)\)
\(=4x\left(2x-y\right)\)
c) \(5u\left(u-v\right)^2+10u^2\left(v-u\right)^2\)
\(=5u\left(u-v\right)^2+10u^2\left(u-v\right)^2\)
\(=5u\left(u-v\right)^2\left(1+2u\right)\)
Trả lời:
a, 3x ( x + 1 )2 - 5x2 ( x + 1 ) + 7 ( x + 1 )
= ( x + 1 )[ 3x ( x + 1 ) - 5x2 + 7 ]
= ( x + 1 )( 3x2 + 3x - 5x2 + 7 )
= ( x + 1 )( - 2x2 + 3x + 7 )
b, ( x + y )( 2x - y ) - ( 3x - y )( y - 2x )
= ( x + y )( 2x - y ) + ( 3x - y )( 2x - y )
= ( 2x - y )( x + y + 3x - y )
= 4x ( 2x - y )
c, 5u ( u - v )2 + 10u2 ( v - u )2
= 5u ( u - v )2 + 10u2 ( u - v )2
= 5u ( u - v )2( 1 + 2u )
a,\(6x^3y^2-9x^2y^3+1^2x^2y^2\)
\(=x^2y^2\left(6x-9y+1\right)\)
b,\(2x\left(x-1\right)+3\left(1-x\right)\)
\(=2x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(2x-3\right)\left(x-1\right)\)
a,
\(6x^3y^2-9x^2y^3+1\cdot x^2\cdot y^2\)
\(=x^2y^2\left(6x-9y+1\right)\)
b,
\(2x\left(x-1\right)+3\left(1-x\right)\)
\(=2x\left(x-1\right)+3\cdot-1\left(x-1\right)\)
\(=2x\left(x-1\right)-3\left(x-1\right)\)
\(=\left(2x-3\right)\left(x-1\right)\)
TL:
\(a,a^{m+2}-a^n\)
\(=a\left(a^{m+1}-a^{n-1}\right)\)
a) \(y^2+2y^2-3y=y.y+y.2y-y.3\)
\(=y\left(y+2y-3\right)\)
b) \(2x^4-x^3+2x^2+1=2x^2.x^2-x^2.x+2x.x^2+1\)
\(=x^2\left(2x^2-x+2x\right)+1=x^2.x\left(2x-1+2\right)+1\)
k mình nha
a. y2+2y2-3y
=y(y+2y-3)
b. 2x4-x3+2x2+1
=2x2(x2+1)-(x3-1)
=2x2(x+1)(x-1)-(x-1)(x2+x+1)
=(x-1)[2x2(x+1)-(x2+x+1)]
=(x-1)(2x3+2x2-x2-x-1)
=(x-1)(2x3+x2-x-1)
2) x(x\(^2\)+2xy +y\(^2\)-9)= x((x+y)\(^2\)-9)= x(x+y-3) (x+y+3)
\(\frac{1}{2}\left(x^2+y^2\right)^2-2x^2y^2=\frac{1}{2}.\left[\left(x^2+y^2\right)^2-4x^2y^2\right]\)
\(=\frac{1}{2}.\left[\left(x^2+y^2\right)^2-\left(2xy\right)^2\right]\)
\(=\frac{1}{2}.\left(x^2+y^2-2xy\right)\left(x^2+y^2+2xy\right)\)
\(=\frac{1}{2}\left(x-y\right)^2.\left(x+y\right)^2\)