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a) \(25.\left(x-1\right)^2-16\left(x+y\right)^2\)
= \(\left(5x-5\right)^2-\left(4x+y\right)^2\)
= \(\left(5x-5-4x-y\right)\left(5x-5+4x+y\right)\)
= \(\left(x-y-5\right)\left(9x+y-5\right)\)
b) \(x^3+3x^2+3x+1-27z^3\)
= \(\left(x+1\right)^3-27z^3\)
= \(\left(x+1-3z\right)\left(x^2+x.3z+9z^2\right)\)
c) \(x^2-2xy+y^2-xz+yz\)
= \(\left(x-y\right)^2-z\left(x-y\right)\)
= \(\left(x-y\right)\left(x-y-z\right)\)
d) \(a^3x-ab+b-x\)
= \(x\left(a^3-1\right)-b\left(a-1\right)\)
= \(x\left(a-1\right)\left(a^2+a+1\right)-b\left(a-1\right)\)
= \(\left(a-1\right)\left(a^2x+ax+x-b\right)\)
f) \(x^2+2x-4y^2-4y\)
= \(x^2+2x+1-\left(4y^2+4y+1\right)\)
= \(\left(x+1\right)^2-\left(2y+1\right)^2\)
= \(\left(x+1-2y-1\right)\left(x+1+2y+1\right)\)
= \(\left(x-2y\right)\left(x+2y+2\right)\)
g) \(xy-4+2x-2y\)
= \(y\left(x-2\right)-2\left(x-2\right)\)
= \(\left(x-2\right)\left(y-2\right)\)
a: \(=\left(5x-5\right)^2-\left(4x-4y\right)^2\)
\(=\left(5x-5-4x+4y\right)\cdot\left(5x-5+4x-4y\right)\)
\(=\left(x+4y-5\right)\left(9x-4y-5\right)\)
b: \(=\left(x+1\right)^3-\left(3z\right)^3\)
\(=\left(x+1-3z\right)\left(x^2+2x+1+3xz+3z+9z^2\right)\)
c: \(=\left(x-y\right)^2-z\left(x-y\right)\)
\(=\left(x-y\right)\left(x-y-z\right)\)
d: \(=x\left(a^3-1\right)-b\left(a-1\right)\)
\(=x\left(a-1\right)\cdot\left(a^2+a+1\right)-b\left(a-1\right)\)
\(=\left(a-1\right)\left(a^2x+ax+1-b\right)\)
Bài 1 :
\(e,x^2+2xy+y^2-2x-2y+1\)
\(=\left(x+y-1\right)^2\)
Bài 2:
\(b,2x^3+3x^2+2x+3=0\)
\(\Leftrightarrow\left(2x^3+2x\right)+\left(3x^2+3\right)=0\)
\(\Leftrightarrow2x\left(x^2+1\right)+3\left(x^2+1\right)=0\)
\(\Leftrightarrow\left(x^2+1\right)\left(2x+3\right)=0\)
\(\Leftrightarrow2x+3=0\left(x^2+1>0\right)\)
\(\Leftrightarrow x=-\dfrac{3}{2}\)
a) x2-y2-2x+2y
=(x+y)(x-y)-2(x-y)
=(x-y)(x+y-2)
b) 2x + 2y - x2 -xy
=2(x+y) - x(x+y)
=(x+y)(2-x)
c) 3a2 - 6ab + 3b2 - 12c2
= 3(a2+b2) -3(2ab+4c2)
= 3(a2+b2-2ab-4c2)
d) x2 - 25 + y2 + 2xy
= x2 + 2xy + y2 -25
= (x+y)2 - 52
= (x+y+5)(x+y-5)
e) x2y - x3 - 9y + 9x
= (9x - x3)+(x2y -9y)
= x(9-x2)+y(x2 - 9)
= x(9-x2)-y(9-x2)
= (9-x2)(x-y)
f) x2-2x-4y2-4y
= x2-4y2-2(x+2y)
=(x+2y)(x-4y)-2(x+2y)
=(x+2y)(x-4y-2)
câu g trùng với câu e
h) x2(x-1)+16(1-x)
= x2(x-1)-16(x-1)
= (x2-16)(x-1)
= (x+4)(x-4)(x-1)
k) \(x^3-x+3x^2+3xt^2+y^3-y\)
\(=\left(x^3+3x^2y+3xy^2+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)^3-\left(x+y\right)\)
\(=\left(x+y\right)\left[\left(x+y\right)^2-1\right]\)
\(=\left(x+y\right)\left(x+y+1\right)\left(x+y-1\right)\)
h) \(a^3-a^2x-ay+xy\)
\(=a^2\left(a-x\right)-y\left(a-x\right)\)
\(=\left(a^2-y\right)\left(a-x\right)\)
a,(x-y)^2-2(x+y)+1 b, x^2-y^2+4x+4 c, 4x^2-y^2+8(y-2)
=(x-y-1)^2 =(x^2+4x+4)-y^2 =4x^2-y^2+8y-16
=(x+2)^2-y^2 =4x^2-(y^2-8y+16)
=(x+2-y)(x+2+y) =4x^2-(y-4)^2
a) (x+y)2-2(x+y)+1=(x+y-1)2
b) x2-y2+4x+4 = (x2+4x+4)-y2=(x+2)2-y2=(x+y+2)(x-y+2)
c)4x2-y2+8(y-2) = 4x2-(y2-8y+16) = (2x)2-(y-4)2=(2x+y-4)(2x-y+4)
d)x3-2x2+2x-4 = x2(x-2)+2(x-2) = (x-2)(x2+2)
e)xy-4+2x-2y=x(y+2) - 2(y+2) = (x-2)(y+2)
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