Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Dùng hằng đẳng thức là xong
a, \(\left(x+y\right)^3-x^3-y^3=x^3+3x^2y+3xy^2+y^3-x^3-y^3\)
\(=3x^2y+3xy^2=3xy\left(x+y\right)\)
b, \(x^2+6xy+9y^2=\left(x+3y\right)^2\)
\(x^2+4x-y^2+4\)
\(=\left(x^2+2.x.2+2^2\right)-y^2\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2-y\right).\left(x+2+y\right)\)
Tham khảo nhé~
\(x^2+4x-y^2+4\)
\(=x^2+4x+4-y^2\)
\(=\left(x^2+4x+4\right)-y^2\)
\(=\left(x^2+2x.2+2^2\right)-y^2\)
\(=\left(x+2\right)^2-y^2\)
\(=\left[\left(x+2\right)+y^2\right].\left[\left(x+2\right)-y^2\right]\)
\(=\left(x+2+y^2\right)\left(x+3-y^2\right)\)
\(e,x^2-y^2+2x+1=\left(x^2+2x+1\right)-y^2\)
\(=\left(x+1\right)^2-y^2=\left(x+1-y\right)\left(x+1+y\right)\)
\(f,x^3+2x^2+2x+1=\left(x^3+1\right)+\left(2x^2+2x\right)\)
\(=\left(x+1\right)\left(x^2-x+1\right)+2x\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x+1+2x\right)\)
\(=\left(x+1\right)\left(x^2+x+1\right)\)
\(x^2-y^2+2x+1\)
\(=\left(x^2+2x+1\right)-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x-y+1\right)\left(x+y+1\right)\)
hk tốt
^^
a) 16x2 - ( x2 + 4 )2
= ( 4x )2 - ( x2 + 4 )2
= [ 4x - ( x2 + 4 ) ][ 4x + ( x2 + 4 ) ]
= ( -x2 + 4x - 4 )( x2 + 4x + 4 )
= [ -( x2 - 4x + 4 ) ]( x + 2 )2
= [ -( x - 2 )2 ]( x + 2 )2
b) ( x + y )3 + ( x - y )3
= [ ( x + y ) + ( x - y ) ][ ( x + y )2 - ( x + y )( x - y ) + ( x - y )2 ]
= ( x + y + x - y )[ x2 + 2xy + y2 - ( x2 - y2 ) + x2 - 2xy + y2 ]
= 2x( 2x2 + 2y2 - x2 + y2
= 2x( x2 + 3y2 )
\(a^3-a^2x-ay+xy\)
\(=a^2\left(a-x\right)-y\left(a-x\right)\)
\(=\left(a-x\right)\left(a^2-y\right)\)
\(4x^2-y^2+4x+1\)
\(=\left(4x^2+4x+1\right)-y^2\)
\(=\left(2x+1\right)^2-y^2=\left(2x-y+1\right)\left(2x+y+1\right)\)
\(x^3-x+y^3-y\)
\(=\left(x^3+y^3\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2\right)-\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-xy+y^2-1\right)\)
a)a3 - a2x - ay +xy
=(a3 - a2x) - (ay - xy)
=a2(a-x) - y(a-x)
=(a-x).(a2 - y)
\(x^2y+xy^2+x^2z+xz^2+y^2z+yz^2+2xyz.\)
\(=x^2.\left(y+z\right)+yz.\left(y+z\right)+x\left(y^2+z^3\right)+2xyz\)
\(=\left(y+z\right).\left(x^2+yz\right)+x\left(y^{^2}+z^2+2yz\right)\)
\(=\left(y+z\right).\left[x.\left(x+2\right)+y.\left(x+2\right)\right]\)
\(=\left(y+z\right).\left(x+z\right).\left(x+y\right)\)
a)\(x^2-y^2-2y-1=x^2-\left(y^2+2y+1\right)=x^2-\left(y+1\right)^2=\left(x-y-1\right)\left(x+y+1\right)\)
b)\(x^2.\left(1-x^2\right)-4+4x^2=x^2.\left(1-x^2\right)-4.\left(1-x^2\right)=\left(1-x^2\right).\left(x^2-2^2\right)\)\(=\left(1-x\right).\left(1+x\right).\left(x-2\right).\left(x+2\right)\)
Tham khảo nhé~
1.\(x^2-7x+6\)\(=x^2-6x-x+6\)\(=x\left(x-6\right)-\left(x-6\right)\)\(=\left(x-1\right)\left(x-6\right)\)
2.\(y^2+xy-2x^2=y+2xy-xy-2x^2\)\(=y\left(y-x\right)+2x\left(y-x\right)\)\(=\left(y+2x\right)\left(y-x\right)\)
Học tốt !
1. x2 - 7x + 6
= x2 - x - 6x + 6
= x( x - 1 ) - 6( x - 1 )
= ( x - 6 )( x - 1 )
2. y2 + xy - 2x2
= y2 - xy + 2xy - 2x2
= y( y - x ) + 2x( y - x )
= ( y + 2x )( y - x )
a) x2 – y2 – 2y – 1 = x2 - (y2 + 2y + 1)
= x2 - (y + 1)2
= (x + y + 1)(x - y - 1)