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xm+3+1+xm+3-(x+1)=xm+3x+xm+3-(x+1)=xm+3(x+1)-(x+1)=(x+1)(xm+3-1)
Ta có : xm+4 + xm+3,-x-1
<=>xm. x4 + xm . x3 - (x+1)
<=> xm+3. (x+1) -( x+1)
<=> (xm+3-1)(x+1)
a: \(x^3z+x^2yz-x^2z^2-xyz^2\)
\(=x^2z\left(x+y\right)-xz^2\left(x+y\right)\)
\(=xz\left(x+y\right)\left(x-z\right)\)
\(x^4+x^2+1\)
\(=\left[\left(x^2\right)^2+2x^2.1+1^2\right]-x^2\)
\(=\left(x^2+1\right)^2-x^2\)
\(=\left(x^2+x+1\right)\left(x^2-x+1\right)\)
\(\left(x^2-8\right)^2+36\)
\(=x^4-16x^2+64+36\)
\(=\left[\left(x^2\right)^2-2.10x^2+10^2\right]-\left(2x\right)^2\)
\(=\left(x^2-10\right)^2-\left(2x\right)^2\)
\(=\left(x^2-10-2x\right)\left(x^2-10+2x\right)\)
\(4x^4+81\)
\(=\left[\left(2x^2\right)^2+2.2x^2.9+9^2\right]-\left(6x\right)^2\)
\(=\left(2x^2+9\right)-\left(6x\right)^2\)
\(=\left(2x^2+9-6x\right).\left(2x^2+9+6x\right)\)
Tham khảo nhé~
M = x9 - x7 + x6 - x5 - x4 + x3 - x2 + 1
= ( x9 - x7 ) + ( x6 - x4 ) - ( x5 - x3 ) - ( x2 - 1 )
= x7( x2 - 1 ) + x4( x2 - 1 ) - x3( x2 - 1 ) - ( x2 - 1 )
= ( x2 - 1 )( x7 + x4 - x3 - 1 )
= ( x - 1 )( x + 1 )[ x4( x3 + 1 ) - ( x3 + 1 ) ]
= ( x - 1 )( x + 1 )( x3 + 1 )( x4 - 1 )
= ( x - 1 )( x + 1 )( x + 1 )( x2 - x + 1 )( x2 - 1 )( x2 + 1 )
= ( x + 1 )2( x - 1 )( x2 - x + 1 )( x - 1 )( x + 1 )( x2 + 1 )
= ( x + 1 )3( x - 1 )2( x2 + 1 )( x2 - x + 1 )
B1:
[(m+n)+(2m-3n)]^2
= (m+n)^2 + 2(m+n)(2m-3n) + (2m-3n)^2
= m^2 +2mn +n^2 + 4m^2 - 6mn + 4mn - 6n^2 + 4m^2 - 12mn + 9n^2
= 9m^2 - 12mn + 4n^2
B2,3
bn lm theo hdt ( a +b + c) ^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc nha
Nhớ mình nha mình âm diểm rồi:
M=(x+2)(x+3)(x+4)(x+5)-24
M=(x2+3x+2x+6)(x2+5x+4x+20)-24
M=(x2+5x+6)(x2+9x+20)-24
M=x4+9x3+20x2+5x3 +14x+100x+6x2+54x+120-24
M=x4+14x3+26x2+168x+96
x4 + x3 + 2x2 + x + 1
= (x4 + 2x2 + 1) + (x3 + x)
= (x2 + 1)2 + x (x2 + 1)
= (x2 + 1) ( x2 + 1 + x)
= (x2 + 1) (x + 1)2
\(=1-4x^2-x^3+4x\)
\(=-\left(x-1\right)\left(x^2+x+1\right)-4x\left(x-1\right)\)
\(=\left(x-1\right)\left(-x^2-x-1-4x\right)\)
\(=\left(x-1\right)\left(-x^2-5x-1\right)\)
(x^m+2)+(x^m) = 2xm+2 = 2(xm+1)
(x^x+1)-(x^x)-1 = xx+1-xx-1 = 0
(m^4)-(n^4) = (m2)2-(n2)2 = (m2-n2)(m2+n2)