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a) \(\left(x^2-x+2\right)^2+\left(x-2\right)^2\)
\(=\left(x^4-2x^3+5x^2-4x+4\right)+\left(x^2-4x+4\right)\)
\(=x^4-2x^3+6x^2-8x+8\)
\(=\left(x^4-2x^3+2x^2\right)+\left(4x^2-8x+8\right)\)
\(=x^2\left(x^2-2x+2\right)+4\left(x^2-2x+2\right)\)
\(=\left(x^2+4\right)\left(x^2-2x+2\right)\)
\(x^4-9x^3+28x^2-36x+16\)
\(=x^4-x^3-8x^3+8x^2+20x^2-20x-16x+16\)
\(=\left(x^4-x^3\right)-\left(8x^3-8x^2\right)+\left(20x^2-20x\right)-\left(16x-16\right)\)
\(=x^3\left(x-1\right)-8x^2\left(x-1\right)+20x\left(x-1\right)-16\left(x-1\right)\)
\(=\left(x-1\right)\left(x^3-8x^2+20x-16\right)\)
\(=\left(x-1\right)\left(x^3-2x^2-6x^2+12x+8x-16\right)\)
\(=\left(x-1\right)[x^2\left(x-2\right)-6x\left(x-2\right)+8\left(x-2\right)]\)
\(=\left(x-1\right)\left(x-2\right)\left(x^2-6x+8\right)\)
\(=\left(x-1\right)\left(x-2\right)\left(x^2-4x-2x+8\right)\)
\(=\left(x-1\right)\left(x-2\right)[x\left(x-4\right)-2\left(x-4\right)]\)
\(=\left(x-1\right)\left(x-2\right)\left(x-2\right)\left(x-4\right)\)
\(=\left(x-1\right)\left(x-2\right)^2\left(x-4\right)\)
\(x^5+y^5-\left(x+y\right)^5\)
\(=x^5+y^5-\left(x^5+5x^4y+10x^3y^2+10x^2y^3+8xy^4+y^5\right)\)
\(=-5xy\left(x^3+2x^2y+2xy^2+y^3\right)\)
\(=-5xy\left[\left(x+y\right)\left(x^2-xy+y^2\right)+2xy\left(x+y\right)\right]\)
\(=-5xy\left(x+y\right)\left(x^2+xy+y^2\right)\)
h)Ta có : \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)
\(=\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24\)
Đặt\(x^2+7x+11=y\)
\(=>p\left(x\right)=\left(y-1\right)\left(y+1\right)-24=y^2-1-24=y^2-25=\left(y-5\right)\left(y+5\right)\)
Thay \(y=x^2+7x+11\) vào ta có : \(p\left(x\right)=\left(x^2+7x+11-5\right)\left(x^2+7x+11+5\right)=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)
\(f)m\left(x\right)=x^6+27=\left(x^2+3\right)\left(x^4-3x^2+9\right)\)
e)\(\left(x^2+x\right)^2+4\left(x^2+x\right)-12=\left(x^2+x\right)^2-2\left(x^2+x\right)+6\left(x^2+x\right)-12=\left(x^2+x\right)\left(x^2+x-2\right)+6\left(x^2+x-12\right)\)
\(=\left(x^2+x+6\right)\left(x^2+x-2\right)=\left(x^2+x+6\right)\left(x^2-x+2x-2\right)=\left(x^2+x+6\right)\left[x\left(x-1\right)+2\left(x-1\right)\right]=\left(x^2+x+6\right)\left(x-1\right)\left(x+2\right)\)
a)A=(x2+2x)+9x2+18x+20
=(x2+2x)+9(x2+2x)+20
Đặt t=x2+2x đc:
t+9t+20=10t+20=10(t+2)
Thay t=x2+2x vào đc:
10(x2+2x+2)
a. \(=x^3+2^3+1^3-x^3\)
\(=\left(x^3-x^3\right)+8+1\)
\(=0+8+1\)
\(=9\)
Bài 1 :
a) ( x + 2 )( x2 - 2x + 4 ) + (1 - x)(1+x+ + x2 )
= ( x3 - 8 ) + ( 1 - x3 )
= x3 - 8 + 1 - x3
= 7
b) 7x( 4x - 2) - ( x - 3)( x+1 ) + 16x
= 28x2 - 14x - x2 - x + 3x + 3 + 16x
= 27x2 + 3