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\(4x^4-9x^2\)
\(=\left(2x^2\right)^2-\left(3x\right)^2\)
\(=\left(2x^2-3x\right)\left(2x^2+3x\right)\)
\(x^3-x^2-x+1\)
\(=x^2\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-1\right)\)
\(a.\left(8x^4-4x^3+x^2\right):2x^2=4x^2-2x+\frac{1}{2}\)
\(b.\left(2x^4-x^3+3x^2\right):\left(-\frac{1}{3x^2}\right)=-6x^6+3x^5-9x^4\)
\(c.\left(-18x^3y^5+12x^2y^2-6xy^3\right):6xy=-3x^2y^4+2xy-y^2\)
\(d.\left(\frac{3}{4x^3y^6}+\frac{6}{5x^4y^5}-\frac{9}{10x^5y}\right):-\frac{3}{5x^3y}=-\frac{5}{4y^5}-\frac{2}{xy^4}-\frac{3}{2x^2}\)
b)x2+2xy+y2-16=(x+y)2-42=(x+y+4)(x+y-4)
c)3x2+5x-3xy-5y=x(3x+5)-y(3x+5)=(3x+5)(x-y)
d)4x2-6x3y-2x2+8x=2x(2x-3x2y-x+4)
e)x2-4-2xy+y2=(x2-2xy+y2)-4=(x-y)2-22=(x-y-2)(x-y+2)
k)x2-y2-z2-2yz=x2-(y+z)2=(x-y-z)(x+y+z)
m)6xy+5x-5y-3x2-3y2=3(x2-2xy+y2)+5(x-y)=3(x-y)2+5(x-y)=(x-y)(3x-3y+5)
vào bệnh viện hoặc đến nơi khám chữa bệnh gần nhà nhất ko kịp thì die
a)x^2-(a+b)x+ab
= x^2 - ax - bx + ab
= (x^2 - ax) - (bx - ab)
= x(x-a) - b(x-a)
= (x-b)(x-a)
b)7x^3-3xyz-21x^2+9z
=
c)4x+4y-x^2(x+y)
= 4(x + y) - x^2(x+y)
= (4-x^2) (x+y)
= (2-x)(2+x)(x+y)
d) y^2+y-x^2+x
= (y^2 - x^2) + (x+y)
= (y-x)(y+x)+ (x+y)
= (y-x+1) (x+y)
e)4x^2-2x-y^2-y
= [(2x)^2 - y^2] - (2x +y)
= (2x-y)(2x+y) - (2x+y)
= (2x -y -1)(2x+y)
f)9x^2-25y^2-6x+10y
=
\(10x\left(x-y\right)-6y\left(y-x\right)\)
\(=10x\left(x-y\right)+6x\left(x-y\right)\)
\(=\left(10x+6x\right)\left(x-y\right)\)
\(c,3x^2+5y-3xy-5x\)
\(=\left(3x^2-3xy\right)+\left(5y-5x\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(3x-5\right)\left(x-y\right)\)
\(e,27+27x+9x^2=3\left(9+9x+x^2\right)\)
a^2-25-2ab+b^2
= (a^2 - 2ab + b^2 ) - 5^2
= (a -b)^2 - 5^2 = ( a - b - 5 ) ( a - b + 5 )
5x^2-6xy+y^2
= (3x)^2 - 2.3x.y + y^2 - (2x)^2
= (3x - y)^2 - (2x)^2
= ( 3x - y - 2x ) ( 3x - y + 2x ) = ( x - y) ( 5x - y )
2x^3-8x^2+8x
= 2x^3 - 4x^2 - 4x^2 + 8x
= 2x^2(x - 2) - 4x(x-2)
= (2x^2 - 4x)(x-2)
= 2x(x-2)(x-2) = 2x .(x-2)^2
5x-5y-3x^2+6xy-3y^2
=5(x - y) - 3(x^2 - 2xy + y^2 )
= 5(x-y) - 3(x-y)^2 = (x-y)[ 5 - 3(x-y) ]
4x^4-9x^2
= (2x^2)^2 - (3x)^2
= (2x^2 - 3x)(2x^2 + 3x)
= x(2x - 3)x(2x + 3 ) = x^2(2x - 3)(2x + 3 )
a) \(a^2-25-2ab+b^2\)
\(=\left(a-b\right)^2-25\)
\(=\left(a-b-5\right)\left(a-b+5\right)\)
b) \(5x^2-6xy+y^2\)
\(=\left(3x\right)^2-2.3x.y+y^2-\left(2x\right)^2\)
\(=\left(3x-y\right)^2-\left(2x\right)^2\)
\(=\left(3x-y-2x\right)\left(3x-y+2x\right)\)
\(=\left(x-y\right)\left(5x-y\right)\)
c) \(2x^3-8x^2+8x\)
\(=2x^3-4x^2-4x^2+8x\)
\(=2x^2\left(x-2\right)-4x\left(x-2\right)\)
\(=2x\left(x-2\right)\left(x-2\right)\)
\(=2x\left(x-2\right)^2\)
d) \(5x-5y-3x^2+6xy-3y^2\)
\(=5\left(x-y\right)-3\left(x^2-2xy+y^2\right)\)
\(=5\left(x-y\right)-3\left(x-y\right)^2\)
\(=\left(x-y\right)\left[5-3\left(x-y\right)\right]\)
e) \(4x^4-9x^2\)
\(=\left(2x^2\right)^2-\left(3x\right)^2\)
\(=\left(2x^2-3x\right)\left(2x^2+3x\right)\)
\(=x\left(2x-3\right).x\left(2x+3\right)\)
\(=x^2\left(2x-3\right)\left(2x+3\right)\)
f) \(x^8+4\)
\(=\left(x^4\right)^2+2.x^4.2+2^2-2.x^4.2\)
\(=\left(x^4+2\right)^2-4x^4\)
\(=\left(x^4+2\right)^2-\left(2x^2\right)^2\)
\(=\left(x^4+2-2x^2\right)\left(x^4+2+2x^2\right)\)
i) \(4x^2-y^2+4x+1\)
\(=\left(2x\right)^2+2.2x+1-y^2\)
\(=\left(2x+1\right)^2-y^2\)
\(=\left(2x+1-y\right)\left(2x+1+y\right)\)
j) \(3x^2-7x+10\)
\(=3\left(x^2-\dfrac{7}{3}x+\dfrac{10}{3}\right)\)
\(=3\left(x^2-2.x.\dfrac{7}{6}+\dfrac{49}{36}-\dfrac{49}{36}+\dfrac{10}{3}\right)\)
\(=3\left[\left(x-\dfrac{7}{6}\right)^2+\dfrac{71}{36}\right]\)
g) \(x^5+x+1\)
\(=x^5+x^4+x^3-x^4-x^3-x^2+x^2+x+1\)
\(=\left(x^5+x^4+x^3\right)-\left(x^4+x^3+x^2\right)+\left(x^2+x+1\right)\)
\(=x^3\left(x^2+x+1\right)-x^2\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^3-x^2-1\right)\)
h) \(x^4+2019x^2+2018x+2019\)
\(=\left(x^4-x\right)+\left(2019x^2+2019x+2019\right)\)
\(=x\left(x^3-1\right)+2019\left(x^2+x+1\right)\)
\(=x\left(x-1\right)\left(x^2+x+1\right)+2019\left(x^2+x+1\right)\)
\(=\left(x^2+x+1\right)\left[x\left(x-1\right)+2019\right]\)
\(=\left(x^2+x+1\right)\left(x^2-x+2019\right)\)