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a) \(4x^2-12x+9=\left(2x\right)^2-2.2x.3+3^2=\left(2x-3\right)^2\)
b) \(4x^2+4x+1=\left(2x\right)^2+2.2x.1+1^2=\left(2x+1\right)^2\)
c) \(1+12x+36x^2=1^2+2.6x.1+\left(6x\right)^2=\left(1+6x\right)^2\)
d) \(9x^2-24xy+16y^2=\left(3x\right)^2-2.3x.4y+\left(4y\right)^2=\left(3x-4y\right)^2\)
f) \(-x^2+10x-25=-\left(x^2-10x+25\right)=-\left(x-5\right)^2\)
g) \(-16a^4b^6-24a^5b^5-9a^6b^4=-\left(16a^4b^6+24a^5b^5+9a^6b^4\right)\)
\(=-\left[\left(4a^2b^3\right)^2+2.4a^2b^3.3a^3b^2+\left(3a^3b^2\right)^2\right]\)
\(=-\left(4a^2b^3+3a^3b^2\right)^2\)
h) \(25x^2-20xy+4y^2=\left(5x\right)^2-2.5x.2y+\left(2y\right)^2\) \(=\left(5x-2y\right)^2\)
i) \(25x^4-10x^2y+y^2=\left(5x^2\right)^2-2.5x^2.y+y^2=\left(5x^2-y\right)^2\)
\(4x^2+4x+1\)
\(=\left(2x\right)^2+2.2x.1+1\)
\(=\left(2x+1\right)^2\)
\(1+12x+36x^2\)
\(=1+2.6x+\left(6x\right)^2\)
\(=\left(1+6x\right)^2\)
a) 5x3 - 40 = 5( x3 - 8 ) = 5( x - 2 )( x2 + 2x + 4 )
b) x2z + 4xyz + 4y2z = z( x2 + 4xy + 4y2 ) = z( x + 2y )2
c) 4x2 - y2 - 6x + 3y = ( 4x2 - y2 ) - ( 6x - 3y ) = ( 2x - y )( 2x + y ) - 3( 2x - y ) = ( 2x - y )( 2x + y - 3 )
d) x2 + 2x - 4y2 + 1 = ( x2 + 2x + 1 ) - 4y2 = ( x + 1 )2 - ( 2y )2 = ( x - 2y + 1 )( x + 2y + 1 )
e) 3x2 - 3y2 - 12x + 12y = 3( x2 - y2 - 4x + 4y ) = 3[ ( x2 - y2 ) - ( 4x - 4y ) ] = 3[ ( x - y )( x + y ) - 4( x - y ) ] = 3( x - y )( x + y - 4 )
f) x3 + 5x2 + 4x + 20 = x2( x + 5 ) + 4( x + 5 ) = ( x + 5 )( x2 + 4 )
g) x3 - x2 - 25x + 25 = x2( x - 1 ) - 25( x - 1 ) = ( x - 1 )( x2 - 25 ) = ( x - 1 )( x - 5 )( x + 5 )
a) \(5x^3-40=5\left(x^3-8\right)=5\left(x-2\right)\left(x^2+2x+4\right)\)
b) \(x^2z+4xyz+4y^2z=z\left(x^2+4xy+4y^2\right)=z\left(x+2y\right)^2\)
c) \(4x^2-y^2-6x+3y=\left(4x^2-y^2\right)-\left(6x-3y\right)\)
\(=\left(2x-y\right)\left(2x+y\right)-3\left(2x-y\right)=\left(2x-y\right)\left(2x+y-3\right)\)
d) \(x^2+2x-4y^2+1=x^2+2x+1-4y^2\)
\(=\left(x+1\right)^2-4y^2=\left(x+2y+1\right)\left(x-2y+1\right)\)
e) \(3x^2-3y^2-12x+12y=3\left(x^2-y^2-4x+4y\right)\)
\(=3\left[\left(x^2-y^2\right)-\left(4x-4y\right)\right]=3\left[\left(x-y\right)\left(x+y\right)-4\left(x-y\right)\right]\)
\(=3\left(x-y\right)\left(x+y+4\right)\)
f) \(x^3+5x^2+4x+20=\left(x^3+5x^2\right)+\left(4x+20\right)\)
\(=x^2.\left(x+5\right)+4\left(x+5\right)=\left(x^2+4\right)\left(x+5\right)\)
g) \(x^3-x^2-25x+25=\left(x^3-x^2\right)-\left(25x-25\right)\)
\(=x^2\left(x-1\right)-25\left(x-1\right)=\left(x-1\right)\left(x^2-25\right)\)
\(=\left(x-1\right)\left(x-5\right)\left(x+5\right)\)
4x2 -6x= 2x(2x-3)
b) 3x3 -6x2y -24xy + 12x2 = \(3x\left(x^2-2xy-8y+4x\right)\)
c) x2 -25 + y2 + 2xy\(=x^2+2xy+y^2-25\)\(=\left(x+y\right)^2-5^2\)
=>\(\left(x+y+5\right)\left(x+y-5\right)\)
Bài 1:
a) 25\(x^2\) - 0,09
= \(\left(5x\right)^2-0,3^2\)
= (5x - 0,3) (5x +0,3)
Bài 5:
a: \(=\left(2x-3\right)^2\)
b: \(=\left(2x+1\right)^2\)
c: \(=\left(6x+1\right)^2\)
d: \(=\left(3x-4y\right)^2\)
e: \(=\left(\dfrac{1}{2}x-2y\right)^2\)
f: \(=-\left(x-5\right)^2\)
a) \(4x^2-12x+9=\left(2x\right)^2-2\cdot2x\cdot3+3^2=\left(2x-3\right)^2\)
b) \(4x^2+4x+1=\left(2x\right)^2+2\cdot2x\cdot1+1^2=\left(2x+1\right)^2\)
c) \(1+12x+36x^2=1^2+2\cdot1\cdot6x+\left(6x\right)^2=\left(1+6x\right)^2\)
d) \(9x^2-24xy+16y^2=\left(3x\right)^2-2\cdot3x\cdot4y+\left(4y\right)^2=\left(3x-4y\right)^2\)
e) \(8x^3+1=\left(2x\right)^3+1^3=\left(2x+1\right)\left(4x^2+2x+1\right)\)
f) \(-8x^3+27=3^3-\left(2x\right)^3=\left(3-2x\right)\left(9+6x+4x^2\right)\)
Bài 8:
b. 1+8x6y3 = 13+23(x2)3y3 = 13+(2x2y)3
= (1+2x2y)(1-2x2y+4x4y2)
e. 27x3+\(\dfrac{y^3}{8}\)\(=\left(3x\right)^3+\left(\dfrac{y}{2}\right)^3\)
= (3x+\(\dfrac{y}{2}\))(9x2-\(\dfrac{3xy}{2}\)+\(\dfrac{y^2}{4}\))
Bài 9:
c. 1- 9x +27x2 -27x3 = 13-3.12.3x+3.(3x)2-(3x)3
= (1-3x)3
d. x3+\(\dfrac{3}{2}x^2\)+\(\dfrac{3}{4}x+\dfrac{1}{8}\) = x3+\(3x^2.\dfrac{1}{2}\)+\(3x.\dfrac{1}{4}+\left(\dfrac{1}{2}\right)^3\)
= (x+\(\dfrac{1}{2}\))3
f. x2 - 2xy +y2 -4m2 +4m.n - n2 = (x2 - 2xy +y2)-((2m)2 -2.2m.n + n2)
= (x-y)2-(2m-n)2 = (x-y-2m+n)(x-y+2m-n)
a) Ta có: \(\left(4x^2-12x+9\right)-1\)
\(=\left(2x-3\right)^2-1^2\)
\(=\left(2x-3-1\right)\left(2x-3+1\right)\)
\(=\left(2x-4\right)\left(2x-2\right)\)
\(=4\left(x-2\right)\left(x-1\right)\)
b) Ta có: \(\left(\frac{x^2}{4}+2xy+4y^2\right)-25\)
\(=\left[\left(\frac{x}{2}\right)^2+2\cdot\frac{x}{2}\cdot2y+\left(2y\right)^2\right]-5^2\)
\(=\left(\frac{x}{2}+2y\right)^2-5^2\)
\(=\left(\frac{x}{2}+2y-5\right)\left(\frac{x}{2}+2y+5\right)\)
c) Ta có: \(1+12x+35x^2\)
\(=35x^2+12x+1\)
\(=35x^2+5x+7x+1\)
\(=5x\left(7x+1\right)+\left(7x+1\right)\)
\(=\left(7x+1\right)\left(5x+1\right)\)
d) Ta có: \(9x^2-24xy+15y^2\)
\(=9x^2-9xy-15xy+15y^2\)
\(=9x\left(x-y\right)-15y\left(x-y\right)\)
\(=\left(x-y\right)\left(9x-15y\right)\)
\(=3\left(x-y\right)\left(3x-5y\right)\)
e) Ta có: \(25x^2-20xy+3y^2\)
\(=25x^2-15xy-5xy+3y^2\)
\(=5x\left(5x-3y\right)-y\left(5x-3y\right)\)
\(=\left(5x-3y\right)\left(5x-y\right)\)
f) Ta có: \(24x^4-10x^2y+y^2\)
\(=24x^4-4x^2y-6x^2y+y^2\)
\(=4x^2\left(6x^2-y\right)-y\left(6x^2-y\right)\)
\(=\left(6x^2-y\right)\left(4x^2-y\right)\)