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a: \(=9xy\left(y-2x\right)\)
b: \(=2\left(3x^2-y\right)\)
c: \(=7x\left(x-y\right)+14y\left(x-y\right)=7\left(x-y\right)\left(x+2y\right)\)
d: \(=\left(\sqrt{7}-x\right)\left(\sqrt{7}+x\right)\)
e: \(=\left(x+4\right)^2\)
f: \(=\left(1-3x\right)\left(1+3x+9x^2\right)\)
g: \(=\left(x-3\right)^3\)
\(a.9xy^2-18x^2y=9xy\left(y-2x\right)\)
\(b.6x^2-2y=2\left(3x^2-y\right)\)
\(c.7x\left(x-y\right)-14y\left(y-x\right)=7x\left(x-y\right)+14y\left(x-y\right)=7\left(x-y\right)\left(x+2y\right)\)
\(d.7-x^2=\left(\sqrt{7}-x\right)\left(\sqrt{7}+x\right)\)
\(e.16+8x+x^2=\left(x+4\right)^2=\left(x+4\right)\left(x+4\right)\)
\(f.1-27x^3=\left(1-3x\right)\left(1+3x+9x^2\right)\)
\(g.x^3-9x^2+27x-27=\left(x-3\right)^3=\left(x-3\right)\left(x-3\right)\left(x-3\right)\)
\(h.\left(x+2y\right)^2-16y^2=\left(x+2y-4y\right)\left(x+2y+4y\right)=\left(x-2y\right)\left(x+6y\right)\)
\(i.x^3-64y^3=\left(x-4y\right)\left(x^2+4xy+16y^2\right)\)
\(\left(x-1\right)^2-25\)
\(=x^2-2x+1-25\)
\(=x^2-2x-24\)
\(=x^2-6x+4x-24\)
\(=x.\left(x-6\right)+4.\left(x-6\right)\)
\(=\left(x+4\right).\left(x-6\right)\)
a, \(1-2y+y^2=\left(y+1\right)^2=\left(y+1\right)\left(y+1\right)\)
b, \(\left(x+1\right)^2-25=\left(x+1\right)^2-5^2=\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)
c, \(1-4x^2=1^2-\left(2x\right)^2=\left(1-2x\right)\left(1+2x\right)\)
d, \(8-27x^3=2^3-\left(3x\right)^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)
Bài làm:
a, 1-4x2
=1-(2x)2
=(1-2x).(1+2x)
b, 8-27x3
=23-(3x)3
=(2-3x).(4+6x+9x2)
Các câu còn lại bạn dùng hằng đẳng thức là phân tích được ra thôi
1 - 4x^2
= 1^2 - ( 2x )^2
= ( 1 - 2x ) ( 1 + 2x )
8 - 27x^ 3
= 2^3 - ( 3x )^3
= ( 2 - 3x ) [ 2^2 + 2 * 3x + ( 3x )^2 ]
= ( 2 - 3x ) ( 4 + 6x + 9x^2 )
= ( 2 - 3x ) ( 9x^2 + 6x + 4 )
27 + 27x + 9x^2 + x^3
= x^3 + 9x^2 + 27x + 27
= x^3 + 3x^2 + 6x^2 + 18x + 9x + 27
= x^2 ( x + 3 ) + 6x ( x + 3 ) + 9 ( x + 3 )
= ( x + 3 ) ( x^2 + 6x + 9 )
= ( x + 3 ) ( x + 3 )^2
= ( x + 3 )^3
x^2 + 4x - 5
= x^2 - x + 5x - 5
= x ( x - 1 ) + 5 ( x - 1 )
= ( x + 1 ) ( x - 5 )
a: \(5x-20y=5\left(x-4y\right)\)
b: \(x^2+x^2y+x^2y^2=x^2\left(1+y+y^2\right)\)
c: \(x\left(x+y\right)-\left(5x+5y\right)=\left(x+y\right)\left(x-5\right)\)
d: \(5\left(x-y\right)+y\left(x-y\right)=\left(x-y\right)\left(y+5\right)\)
\(10x\left(x-y\right)-6y\left(y-x\right)\)
\(=10x\left(x-y\right)+6x\left(x-y\right)\)
\(=\left(10x+6x\right)\left(x-y\right)\)
\(c,3x^2+5y-3xy-5x\)
\(=\left(3x^2-3xy\right)+\left(5y-5x\right)\)
\(=3x\left(x-y\right)-5\left(x-y\right)\)
\(=\left(3x-5\right)\left(x-y\right)\)
\(e,27+27x+9x^2=3\left(9+9x+x^2\right)\)
d)5.(x-y)-y(x-y)
=(x-y)(5-y)
e) y.(x-z)+7(z-x)
=y.(x-z)-7(x-z)
=(x-z)(y-7)