Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a)x4+2x2+1=(x2)2+2.x2.1+12=(x2+1)2
b) 4x2-12xy+9y2=(2x)2-2.2x.3y+(3y)2=(2x-3y)2
c) -x2-2xy-y2= -(x2+2xy+y2)=-(x+y)2
d) (x+y)2-2(x+y)+1= (x+y-1)2
e)x3-3x2+3x-1= (x3-1)+(-3x2+3x)=(x-1)(x2+x+1)-3x(x-1)
=(x-1)(x2-2x+1)=(x-1)3
g) x3+6x2+12x+8= (x+2)3
h) x3+1-x2-x= (x+1)(x2-x+1)-(x2+x)=(x+1)(x2-x+1)-x(x+1)
=(x+1)(x-1)2
k) (x+y)3-x3-y3= (x+y)3-(x3+y3)=(x+y)3-(x+y)(x2-xy+y2)
= (x+y)[(x+y)2-(x2-xy+y2)]
= 3xy(x+y)
a. \(\left(x+y\right)^3+\left(x-y\right)^3\)
\(=x^3+3x^2y+3xy^2+y^3+x^3-3x^2y+3xy^2-y^3\)
\(=2x^3+6xy^2\)
\(=2x\left(x^2+6y^2\right)\)
b. \(x^3-y^3+2x^2-2y^2\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)+2\left(x^2-y^2\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)+2\left(x+y\right)\left(x-y\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2+2x+2y\right)\)
c. \(x^3-y^3-3x^2+3x-1\)
\(=\left(x^3-3x^2+3x-1\right)-y^3\)
\(=\left(x-1\right)^3-y^3\)
\(=\left(x-1-y\right)\left[\left(x-1\right)^2+\left(x-1\right)y+y^2\right]\)
\(=\left(x-y-1\right)\left(x^2+y^2+xy-2x-y+1\right)\)
a/ \(=3y^2-6y-2x+1\)
b/ \(=-\left(x^3-3x^2+3x-1\right)=-\left(x-1\right)^3\)
c/ \(=\left(2-x\right)^3\)
d/ \(=xy^2+x^2y+3xy+x^2y+x^3+3x^2-3xy-3x^2-9x\)
\(=xy\left(y+x+3\right)+x^2\left(y+x+3\right)-3x\left(y+x+3\right)\)
\(=\left(xy+x^2-3x\right)\left(y+x+3\right)=x\left(y+x-3\right)\left(y+x+3\right)\)
e/ \(=xy-x^2+2x-y^2+xy-2y\)
\(=x\left(y-x+2\right)-y\left(y-x+2\right)=\left(x-y\right)\left(y-x+2\right)\)
a) =(2x+3y-1)2
b)=-(x-1)3
c)=-(x3-6x2+12x-8)=-(x-2)3
d)x3 + 2x2y + xy2 – 9x
= x(x2 + 2xy + y2 -9)
= x[(x2 + 2xy + y2) - 32]
= x[(x + y)2 - 32]
= x (x + y – 3)(x + y + 3)
e) 2x-2y-x2+2xy-y2=2(x-y)-(x-y)2=(x-y)(2-x+y)
a) x2 + 6x + 9 = x2 + 2 . x . 3 + 32 = (x + 3)2
b) 10x – 25 – x2 = -(-10x + 25 +x2) = -(25 – 10x + x2)
= -(52 – 2 . 5 . x – x2) = -(5 – x)2
c) 8x3 - 1/8 = (2x)3 – (1/2)3 = (2x - 1/2)[(2x)2 + 2x . 12 + (1/2)2]
= (2x - 1/2)(4x2 + x + 1/4)
d)1/25x2 – 64y2 = (1/5x)2(1/5x)2- (8y)2 = (1/5x + 8y)(1/5x - 8y)
a,\(xy+3x-7y-21\)
\(=x\left(y+3\right)-7\left(y+3\right)\)
\(=\left(y+3\right)\left(x-7\right)\)
\(b,2xy-15-6x+5y\)
\(=\left(2xy-6x\right)+\left(-15+5y\right)\)
\(=2x\left(y-3\right)-5\left(3-y\right)\)
\(=2x\left(y-3\right)+5\left(y-3\right)\)
\(=\left(y-3\right)\left(2x+5\right)\)
\(a,x^4+2x^2+1=\left(x^2+1\right)^2\)
\(b,4x^2-12xy+9y^2=\left(2x-3y\right)^2\)
\(c,-x^2-2xy-y^2=-\left(x^2+2xy+y^2\right)=-\left(x+y\right)^2\)
\(d,\left(x+y\right)^2-2\left(x+y\right)-1=\left(x+y\right)\left(x+y-2\right)-1\)
e: \(x^3-3x^2+3x-1=\left(x-1\right)^3\)
g: \(=\left(x+2\right)^3\)
h: \(=\left(x+1\right)\left(x^2-x+1\right)+x\left(x+1\right)=\left(x^2+1\right)\left(x+1\right)\)
k: \(=x^3+y^3+3xy\left(x+y\right)-x^3-y^3\)
=3xy(x+y)