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a) x2 + 4x + 3
= x2 + 3x + x +3
= ( x2 + 3 ) + ( x + 3 )
= x ( x + 3 ) + ( x + 3 )
= ( x + 3 ) ( x + 1 )
b) 4x2 - 4x - 3
= 4x2 + 2x - 6x - 3
= ( 4x2 + 2x ) - ( 6x + 3 )
= 2x ( 2x + 1 ) - 3 ( 2x + 1 )
= ( 2x + 1 )( 2x - 3 )
c) x2 - x - 12
= x2 + 3x - 4x - 12
= ( x2 + 3x ) - ( 4x + 12 )
= x ( x + 3 ) - 4 ( x + 3 )
= ( x + 3 ) ( x - 4 )
d) 4x4 - 4x2y2 - 8y4
= 4 ( x4 - x2y2 - 2y4 )
Hk tốt
\(x^4+4\)
\(=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-\left(2x\right)^2\)
\(=\left(2-x^2\right)\left(3x^2+2\right)\)
\(4x^4+4x^2y^2-8y^4\)
\(=4\left(x^4+x^2y^2-2y^4\right)\)
\(=4\left(x^4-x^2y^2+2x^2y^2-2y^4\right)\)
\(=4\left[x^2\left(x^2-y^2\right)+2y^2\left(x^2-y^2\right)\right]\)
\(=4\left(x^2+2y^2\right)\left(x^2-y^2\right)\)
\(=4\left(x^2+2y^2\right)\left(x-y\right)\left(x+y\right)\)
a) \(x^4+4=x^4+4x^2+4-4x^2\)
\(=\left(x^2+2\right)^2-4x^2=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)
b) \(4x^4+4x^2y^2-8y^4=4x^4+4x^2y^2+y^4-9y^4\)
\(=\left(2x^2+y^2\right)^2-9y^4=\left(2x^2+y^2+3y^2\right)\left(2x^2+y^2-3y^2\right)\)
\(=\left(2x^2+4y^2\right)\left(2x^2-2y^2\right)\)
\(=4\left(x^2+2y^2\right)\left(x^2-y^2\right)=4\left(x^2+2y^2\right)\left(x-y\right)\left(x+y\right)\)
a) x^2+4x+3=x^2+x+3x+3=x(x+1)+3(x+1)=(x+1)(x+3)
b) 4x^2+4x-3=4x^2+4x+1-4=(2x+1)^2-4=(2x+1-2)(2x+1+2)=(2x-1)(2x+3)
c) x^2-x-12=x^2-4x+3x-12=x(x-4)+3(x-4)=(x-4)(x+3)
d) 4x^4+4x^2y^2-8y^4=4(x^4+x^2y^2-2y^4)=4(x^4-x^2y^2+2x^2y^2-2y^4)=4(x^2-y^2)(x^2+2y^2)=4(x-y)(x+y)(x^2+2y^2)
a) \(x^2+4x+3\)
\(=x^2+x+3x+3\)
\(=\left(x^2+x\right)+\left(3x+3\right)\)
\(=x\left(x+1\right)+3\left(x+1\right)\)
\(=\left(x+1\right)\left(x+3\right)\)
c) \(x^2-x-12\)
\(=x^2-4x+3x-12\)
\(=\left(x^2-4x\right)+\left(3x-12\right)\)
\(=x\left(x-4\right)+3\left(x-4\right)\)
\(=\left(x-4\right)\left(x+3\right)\)
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)
a, \(x^2+4x+3=x^2+x+3x+3=x\left(x+1\right)+3\left(x+1\right)=\left(x+3\right)\left(x+1\right)\)
b, \(4x^2+4x-3=\left(2x\right)^2+2.2x+1-4=\left(2x+1\right)^2-2^2=\left(2x+1-2\right)\left(2x+1+2\right)=\left(2x-1\right)\left(2x+3\right)\)
c, \(x^2-x-12=x^2-x+\dfrac{1}{4}-\dfrac{49}{4}=\left(x-\dfrac{1}{2}\right)^2-\left(\dfrac{7}{2}\right)^2=\left(x-\dfrac{1}{2}-\dfrac{7}{2}\right)\left(x-\dfrac{1}{2}+\dfrac{7}{2}\right)=\left(x-4\right)\left(x+3\right)\)
d, \(4x^4+4x^2y^2-8y^4=\left(2x^2\right)^2+2.2x^2y^2+\left(y^2\right)^2-9y^4=\left(2x^2+y^2\right)^2-\left(3y^2\right)^2=\left(2x^2+y^2-3y^2\right)\left(2x^2+y^2+3y^2\right)=\left(2x^2-2y^2\right)\left(2x^2+4y^2\right)=4\left(x+y\right)\left(x-y\right)\left(x^2+2y^2\right)\)