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b)\(\left(x^2-8\right)^2+36\)
\(=x^4-16x^2+100\)
\(=x^4+20x^2+100-36x^2\)
\(=\left(x^2+10\right)^2-36x^2\)
\(=\left(x^2-6x+10\right)\left(x^2+6x+10\right)\)
c)81x4+4
=81x4+36x2+4-36x2
=(9x2+2)2-(6x)2
=(9x2+6x+2)(9x2-6x+2)
b) \(x^3-3x^2+2\)
\(=x^3-2x^2-x^2+2\)
\(=x^2\left(x-2\right)-\left(x-2\right)\left(x+2\right)\)
\(=\left(x^2-x-2\right)\left(x-2\right)\)
c) \(x^4y^4+64\)
\(=x^4y^4+16x^2+64-16x^2\)
\(=\left(x^2y^2+8\right)^2-\left(4x\right)^2\)
\(=\left(x^2y^2-4x+8\right)\left(x^2y^2+4x+8\right)\)
d) \(x^8+x^7+1\)
\(=x^8+x^7+x^6-x^6+1\)
\(=x^6\left(x^2+x+1\right)-\left(x^3-1\right)\left(x^3+1\right)\)
\(=x^6\left(x^2+x+1\right)-\left(x-1\right)\left(x^2+x+1\right)\left(x^3+1\right)\)
\(=\left(x^2+x+1\right)\left[x^6-\left(x-1\right)\left(x^3+1\right)\right]\)
\(=\left(x^2+x+1\right)\left[x^6-x^4-x+x^3-1\right]\)
BÀI 1:
a) \(x^4+2x^2y+y^2=\left(x^2+y\right)^2\)
b) \(\left(2a+b\right)^2-\left(2b+a\right)^2=\left(2a+b+2b+a\right)\left(2a+b-2b-a\right)\)
\(=\left(3a+3b\right)\left(a-b\right)=3\left(a+b\right)\left(a-b\right)\)
c) \(\left(a^3-b^3\right)+\left(a-b\right)^2=\left(a-b\right)\left(a^2+ab+b^2\right)+\left(a-b\right)^2\)
\(=\left(a-b\right)\left[a^2+ab+b^2+\left(a-b\right)\right]=\left(a-b\right)\left(a^2+ab+b^2+a-b\right)\)
d) \(\left(x^2+1\right)^2-4x^2=\left(x^2+1-2x\right)\left(x^2+1+2x\right)=\left(x-1\right)^2\left(x+1\right)^2\)
e) \(\left(y^3+8\right)+\left(y^2-4\right)=\left(y+2\right)\left(y^2-y+2\right)\)
f) \(1-\left(x^2-2xy+y^2\right)=1-\left(x-y\right)^2=\left(1-x+y\right)\left(1+x-y\right)\)
g) \(x^4-1=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\)
h) ktra lại đề
m) \(\left(x-a\right)^4-\left(x+a\right)^4=-8ax\left(a^2+x^2\right)\)
a)
\((x^2+x)^2+3(x^2+x)+2\)
\(=(x^2+x)^2+(x^2+x)+2(x^2+x)+2\)
\(=(x^2+x)(x^2+x+1)+2(x^2+x+1)\)
\(=(x^2+x+2)(x^2+x+1)\)
b) \(x(x+1)(x+2)(x+3)+1\)
\(=[x(x+3)][(x+1)(x+2)]+1\)
\(=(x^2+3x)(x^2+3x+2)+1\)
\(=(x^2+3x)^2+2(x^2+3x)+1\)
\(=(x^2+3x+1)^2\)
c) \((x^2+x+1)(x^2+3x+1)+x^2\)
\(=(x^2+x+1)[(x^2+x+1)+2x]+x^2\)
\(=(x^2+x+1)^2+2x(x^2+x+1)+x^2\)
\(=(x^2+x+1+x)^2\)
\(=(x^2+2x+1)^2=[(x+1)^2]^2=(x+1)^4\)
d) \((x^2+1)^2-4x(1-x^2)\)
\(=(x^2+1)^2+4x(x^2-1)\)
\(=(x^2+1)^2+(x-1)(4x^2+4x)\)
\(=(x^2+1)^2+(x-1)[4x^2+4+(4x-4)]\)
\(=(x^2+1)^2+(4x^2+4)(x-1)+(4x-4)(x-1)\)
\(=(x^2+1)^2+2(x^2+1)(2x-2)+(2x-2)^2\)
\(=(x^2+1+2x-2)^2=(x^2+2x-1)^2\)
a) 4(x2-y2)-8(x-ay)-4(a2-1)
=> 4x2-4y2-8x+8ay-4a2+4
=> 4(x2-y2-2x+2ay-a2+1)
c) a5+a4+a3 +a2 +a+1
=> a(a4+a3+a2+a+1)+1
Bài 1 :
a) \(x^8+x+1\)
\(=x^8-x^2+\left(x^2+x+1\right)\)
\(=x^2\left(x^6-1\right)+\left(x^2+x+1\right)\)
\(=x^2\left(x^3+1\right)\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(=\left(x^5+x^2\right)\left(x^3-1\right)+\left(x^2+x+1\right)\)
\(=\left(x^5+x^2\right)\left(x-1\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^6-x^5+x^3-x^2\right)\left(x^2+x+1\right)+\left(x^2+x+1\right)\)
\(=\left(x^6-x^5+x^4-x^2+1\right)\left(x^2+x+1\right)\)
b) \(64x^4+y^4\)
\(=\left(8x^2\right)^2+\left(y^2\right)^2+2.8x^2.y^2-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)
Ta có ; x2 - 11x + 24
= x2 - 3x - 8x + 24
= x(x - 3) - (8x - 24)
= x(x - 3) - 8(x - 3)
= (x - 3)(x - 8)
a,(x-y)^2-2(x+y)+1 b, x^2-y^2+4x+4 c, 4x^2-y^2+8(y-2)
=(x-y-1)^2 =(x^2+4x+4)-y^2 =4x^2-y^2+8y-16
=(x+2)^2-y^2 =4x^2-(y^2-8y+16)
=(x+2-y)(x+2+y) =4x^2-(y-4)^2
a) (x+y)2-2(x+y)+1=(x+y-1)2
b) x2-y2+4x+4 = (x2+4x+4)-y2=(x+2)2-y2=(x+y+2)(x-y+2)
c)4x2-y2+8(y-2) = 4x2-(y2-8y+16) = (2x)2-(y-4)2=(2x+y-4)(2x-y+4)
d)x3-2x2+2x-4 = x2(x-2)+2(x-2) = (x-2)(x2+2)
e)xy-4+2x-2y=x(y+2) - 2(y+2) = (x-2)(y+2)
b)\(\left(x^4+16x^2+64\right)-16x^2\)
\(=\left(x^2+8\right)^2-16x^2\)
\(=\left(x^2+4x+8\right)\left(x^2-4x+8\right)\)
c) thêm bớt \(16x^2\)
d)thêm bớt\(36x^2\)
a)\(\left(x^4+4x^2+4\right)-4x^2\)
\(=\left(x^2+2\right)^2-4x^2\)
\(=\left(x^2+2x+2\right)\left(x^2-2x+2\right)\)