Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
F=x2+2xy+y2-x-y-12
= (x + y)^2 - (x + y) - 12
= (x + y)(x + y - 1) - 12
đặt x + y = t
F = t(t - 1) - 12
= t^2 - t - 12
= (t - 4)(t + 3)
G=(x2-3x-1)2-12(x2-3x-1)+27
đăth x^2 - 3x - 1 = t
G = t^2 - 12t + 27
= (t - 3)(t - 9)
có t = x^2 - 3x - 1
thay vào
Câu F ( kiểm tra lại đề )
Câu G . Đặt x^2 -3x-1=t
t^2 -12t+27 ( thực hiện pp tách)
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)
\(Dat:x^2+x=a\Rightarrow....=a^2-2a-15=\left(a-1\right)^2-4^2=\left(a+3\right)\left(a-7\right)\)
\(=\left(x^2+x+3\right)\left(x^2+x-5\right)\)
\(Dat:x+y=a\Rightarrow....=a^2-a-12=\left(a+3\right)\left(a-4\right)=\left(x+y+3\right)\left(x+y-4\right)\)
a) A= \(\left(x^2+x\right)^2-2\left(x^2+x\right)-15\)
Đặt \(x^2+x=a\) .
Khi đó : \(A=a^2-2a-15=a^2-5a+3a-15\)\(=a\left(a-5\right)+3\left(a-5\right)=\left(a+3\right)\left(a-5\right)\)
Mà \(a=x^2+x\) nên \(A=\left(x^2+x+3\right)\left(x^2+x-5\right)\)
b) B = \(x^2+2xy+y^2-x-y-12\) \(=\left(x+y\right)^2-\left(x+y\right)-12\)
Đặt x+y = z.
Khi đó : \(B=z^2-z-12=z^2-4z+3z-12=z\left(z-4\right)+3\left(z-4\right)\)\(=\left(z+3\right)\left(z-4\right)\)
Mà z = x+y nên B = (x+y+3)(x+y-4)
\(Dat:a^2+a+1=b\Rightarrow....=a\left(a+1\right)-12=\left(a+4\right)\left(a-3\right)\)
=
a) \(\left(x^2+x+1\right)\left(x^2+x+2\right)-12\) (1)
Đặt x2 + x +1 = t
Ta có : \(t\left(t+1\right)-12=t^2+t-12=t^2-3t+4t-12\)
\(=t\left(t-3\right)+4\left(t-3\right)=\left(t-3\right)\left(t+4\right)\)
Thay vào (1), ta được : \(\left(x^2+x+1-3\right)\left(x^2+x+1+4\right)=\left(x^2+x-2\right)\left(x^2+x+5\right)\)
\(=\left(x-1\right)\left(x+2\right)\left(x^2+x+5\right)\)
b) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\) (2)
\(=\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
Đặt x2 + 7x + 11 = y
Ta có : \(\left(y-1\right)\left(y+1\right)-24=y^2-1-24=y^2-25=\left(y-5\right)\left(y+5\right)\)
Thay vào (2), ta được : \(\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x-1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
a)
\(=x^2\left(2x+3\right)+\left(2x+3\right)\)
\(=\left(x^2+1\right)\left(2x+3\right)\)
b)
\(=a\left(a-b\right)+a-b\)
\(=\left(a+1\right)\left(a-b\right)\)
c)
\(=2\left(x^2+2x+1-y^2\right)\)
\(=2\left(x+1-y\right)\left(x+1+y\right)\)
d)
\(=x^3\left(x-2\right)+10x\left(x-2\right)\)
\(=x\left(x^2+10\right)\left(x-2\right)\)
e)
\(=x\left(x^2+2x+1\right)\)
\(=x\left(x+1\right)^2\)
f)
\(=y\left(x+y\right)-\left(x+y\right)\)
\(=\left(y-1\right)\left(x+y\right)\)
a,2x3+3x2+2x+3
=(2x3+2x)+(3x2+3)
=2x(x2+1)+3(x2+1)
=(x2+1)(2x+3)
b,a2-ab+a-b
=(a2-ab)+(a-b)
=a(a-b)+(a-b)
=(a-b)(a+1)
c,2x2+4x+2-2y2
=2(x2+2x+1-y2)
=2[(x2+2x+1)-y2 ]
=2[(x+1)2-y2 ]
=2(x+1-y)(x+1+y)
d,x4-2x3+10x2-20x
=(x4-2x3)+(10x2-20x)
=x3(x-2)+10x(x-2)
=(x-2)(x3+10x)
=(x-2)[x(x2+10)]
e,x3+2x2+x
=x(x2+2x+1)
=x(x+1)2
f,xy+y2-x-y
=(xy+y2)-(x-y)
=y(x+y)-(x+y)
=(x+y)(y-1)
B1:
a) \(5\left(x^2+y^2\right)-20x^2y^2\)
\(=5\left(x^2-4x^2y^2+y^2\right)\)
b) \(=2\left(x^8-16\right)=2\left(x^4-4\right)\left(x^4+4\right)=2\left(x^2-2\right)\left(x^2+2\right)\left(x^4+4\right)\)
B2:
a) Đặt \(x^2-3x+1=y\)
=> \(y^2-12y+27\)
\(=\left(y^2-12y+36\right)-9\)
\(=\left(y-6\right)^2-3^2\)
\(=\left(y-9\right)\left(y-3\right)\)
\(=\left(x^2-3x-10\right)\left(x^2-3x-4\right)\)
\(=\left(x+1\right)\left(x-4\right)\left(x^2-3x-10\right)\)
b) Đặt \(x^2+7x+11=t\)
Ta có: \(\left[\left(x+2\right)\left(x+5\right)\right]\cdot\left[\left(x+3\right)\left(x+4\right)\right]-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
\(=\left(t-1\right)\left(t+1\right)-24\)
\(=t^2-25\)
\(=\left(t-5\right)\left(t+5\right)\)
\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
Bài 1.
a) 5( x2 + y2 ) - 20x2y2
= 5x2 + 5y2 - 20x2y2
= 5( x2 + y2 - 4x2y2 )
b) 2x8 - 32
= 2( x8 - 16 )
= 2[ ( x4 )2 - 42 ]
= 2( x4 - 4 )( x4 + 4 )
= 2[ ( x2 )2 - 22 ]( x4 + 2x3 - 2x3 + 2x2 - 4x2 + 2x2 - 4x + 4x + 4 )
= 2( x2 - 2 )( x2 + 2 )[ ( x4 + 2x3 + 2x2 ) - ( 2x3 + 4x2 + 4x ) + ( 2x2 + 4x + 4 ) ]
= 2( x2 - 2 )( x2 + 2 )[ x2( x2 + 2x + 2 ) - 2x( x2 + 2x + 2 ) + 2( x2 + 2x + 2 ) ]
= 2( x2 - 2 )( x2 + 2 )( x2 + 2x + 2 )( x2 - 2x + 2 )
Bài 2.
a) ( x2 - 3x - 1 )2 - 12( x2 - 3x - 1 ) + 27
= [ ( x2 - 3x - 1 )2 - 12( x2 - 3x - 1 ) + 36 ] - 9
= [ ( x2 - 3x - 1 ) - 6 ) ]2 - 9
= ( x2 - 3x - 7 )2 - 32
= ( x2 - 3x - 7 - 3 )( x2 - 3x - 7 + 4 )
= ( x2 - 3x - 10 )( x2 - 3x - 4 )
= ( x2 + 2x - 5x - 10 )( x2 + x - 4x - 4 )
= [ x( x + 2 ) - 5( x + 2 ) ][ x( x + 1 ) - 4( x + 1 ) ]
= ( x + 2 )( x - 5 )( x + 1 )( x - 4 )
b) ( x + 2 )( x + 3 )( x + 4 )( x + 5 ) - 24
= [ ( x + 2 )( x + 5 ) ][ ( x + 3 )( x + 4 ) ] - 24
= [ x2 + 7x + 10 ][ x2 + 7x + 12 ] - 24 (*)
Đặt t = x2 + 7x + 10
(*) <=> t( t + 2 ) - 24
= t2 + 2t - 24
= ( t2 + 2t + 1 ) - 25
= ( t + 1 )2 - 25
= ( t + 1 - 5 )( t + 1 + 5 )
= ( t - 4 )( t + 6 )
= ( x2 + 7x + 10 - 4 )( x2 + 7x + 10 + 6 )
= ( x2 + 7x + 6 )( x2 + 7x + 16 )
= ( x2 + x + 6x + 6 )( x2 + 7x + 16 )
= [ x( x + 1 ) + 6( x + 1 ) ]( x2 + 7x + 16 )
= ( x + 1 )( x + 6 )( x2 + 7x + 16 )
Phân tích đa thức đặt ẩn phụ :
a)
Đặt \(t=x^2-3x-1\)
\(t^2-12t+27\)
\(=t^2-3t-9t+27\)
\(=t\left(t-3\right)-9\left(t-3\right)\)
\(=\left(t-3\right)\left(t-9\right)\)
\(=\left(x^2-3x-1-3\right)\left(x^2-3x-1-9\right)\)
\(=\left(x^2-3x-4\right)\left(x^2-3x-10\right)\)
\(=\left(x^2+x-4x-4\right)\left(x^2-5x+2x-10\right)\)
\(=\left[x\left(x+1\right)-4\left(x+1\right)\right]\left[x\left(x-5\right)+2\left(x-5\right)\right]\)
\(=\left(x+1\right)\left(x-4\right)\left(x+2\right)\left(x-5\right)\)
b,
\(=\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
Đặt \(t=x^2+7x+10\)
\(t\left(t+2\right)-24\)
\(=t^2+2t-24\)
\(=t^2-4t+6t-24\)
\(=t\left(t-4\right)+6\left(t-4\right)\)
\(=\left(t-4\right)\left(t+6\right)\)
\(=\left(x^2+7x+10-4\right)\left(x^2+7x+10+6\right)\)
\(=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)
a,\(5\left(x^2+y^2\right)-20x^2y^2\)
\(=5x^2+5y^2-20x^2y^2\)
\(=5\left(x^2+y^2+x^2y^2\right)\)
Bài 2:
a,\(\left(x^2-3x-1\right)^2-12\left(x^2-3x-1\right)+27\)(*)
Đặt \(x^2-3x-1=0\)
(*)\(=t^2-12t+27\)
\(=t^2-3t-9t+27\)
\(=t\left(t-3\right)-9\left(t-3\right)\)
\(=\left(t-9\right)\left(t-3\right)\)
\(=\left(x^2-3x-10\right)\left(x^2-3x-4\right)\)
b,\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x+1\right)\left(x+4\right)\left(x+2\right)\left(x+3\right)-24\)
\(=\left(x^2+x+4x+4\right)\left(x^2+2x+3x+6\right)-24\)
\(=\left(x^2+5x+4\right)\left(x^2+5x+6\right)-24\)
\(=\left(x^2+5x+5-1\right)\left(x^2+5x+5+1\right)-24\)
\(=\left(x^2+5x+5\right)^2-1^2-24\)
\(=\left(x^2+5x+5\right)^2-25\)
\(=\left(x^2+5x+5\right)^2-5^2\)
\(=\left(x^2+5x\right)\left(x^2+5x+10\right)\)
\(=x\left(x+5\right)\left(x^2+5x+10\right)\)