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a)ta co: 125x^3+y^6=(5x)^3+(y^2)^3=(5x+y^2)(5x-5xy^2+y^2) b)ta co 5xy^2-10xyz+5xz^2=5x(y^2-2yz+z^2)=5x(y-z)^2 (may cau sau gan giong ban tu lam nha)
b) \(5xy^2-10xyz+5xz^2\)
\(=5xy^2-5xyz-5xyz+5xz^2\)
\(=5xy\left(y-z\right)-5xz\left(y-z\right)\)
\(=\left(y-z\right)\left(5xy-5xz\right)\)
\(=5x\left(y-z\right)\left(y-z\right)\)
\(=5x\left(y-z\right)^2\)
Đây, bản full đây thím, tớ thực sự đã kiên nhẫn lắm đấy ...
a)\(4\left(x^2-y^2\right)-8\left(x-ay\right)-4\left(a^2-1\right)=4\left(x^2-y^2-2x+2ay-a^2+1\right)\)
\(=4\left[\left(x^2-2x+1\right)-\left(a^2-2ay+y^2\right)\right]\)
\(=4\left[\left(x-1\right)^2-\left(a-y\right)^2\right]\)
\(=4\left(x-1-a+y\right)\left(x-1+a-y\right)\)
b)\(\left(x+y\right)^3-1-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left[\left(x+y\right)^2+x+y+1\right]-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left(x^2+2xy+y^2+x+y+1\right)-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left(x^2+2xy+y^2+x+y+1-3xy\right)\)
\(=\left(x+y-1\right)\left(x^2-xy+y^2+x+y+1\right)\)
c)\(x^3-1+5x^2-5+3x-3=\left(x-1\right)\left(x^2+x+1\right)+5\left(x^2-1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1\right)+5\left(x-1\right)\left(x+1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1\right)+\left(x-1\right)\left(5x+5\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+1+5x+5+3\right)\)
\(=\left(x-1\right)\left(x^2+6x+9\right)\)
\(=\left(x-1\right)\left(x+3\right)^2\)
d)\(a^5+a^4+a^3+a^2+a+1=a^4\left(a+1\right)+a^2\left(a+1\right)+\left(a+1\right)\)
\(=\left(a+1\right)\left(a^4+a^2+1\right)\)
\(=\left(a+1\right)\left(a^4+2a^2+1-a^2\right)\)
\(=\left(a+1\right)\left[\left(a^2+1\right)^2-a^2\right]\)
\(=\left(a+1\right)\left(a^2-a+1\right)\left(a^2+a+1\right)\)
e)\(x^3-3x^2+3x-1-y^3=\left(x-1\right)^3-y^3\)
\(=\left(x-1-y\right)\left[\left(x-1\right)^2+\left(x-1\right)y+y^2\right]\)
\(=\left(x-1-y\right)\left(x^2-2x+1+xy-y+y^2\right)\)
f)\(5x^3-3x^2y-45xy^2+27y^3=5x\left(x^2-9y^2\right)-3y\left(x^2-9y^2\right)\)
\(=\left(x^2-9y^2\right)\left(5x-3y\right)\)
\(=\left(x-3y\right)\left(x+3y\right)\left(5x-3y\right)\)
g)\(3x^2\left(a-b+c\right)+36xy\left(a-b+c\right)+108y^2\left(a-b+c\right)\)
\(=\left(a-b+c\right)\left(3x^2+36xy+108y^2\right)\)
\(=3\left(a-b+c\right)\left(x^2+12xy+36y^2\right)\)
\(=3\left(a-b+c\right)\left(x+6y\right)^2\)
a/ \(4\left(x^2-y^2\right)-8\left(x-ay\right)-4\left(a^2-1\right)\)
\(=\left(4x^2-8x+4\right)-\left(4y^2-8ay+4a^2\right)\)
\(=\left(2x-2\right)^2-\left(2y-2a\right)^2=\left(2x-2+2y-2a\right)\left(2x-2-2y+2a\right)\)
b/ \(\left(x+y\right)^3-1-3xy\left(x+y-1\right)=\left(x+y-1\right)\left(x^2+y^2+2xy+x+y+1\right)-3xy\left(x+y-1\right)\)
\(=\left(x+y-1\right)\left(x^2+y^2-xy+x+y+1\right)\)
Giải giúp bạn 2 bài tiêu biểu thôi nha
b)(x2+x+1)(x2+x+2)-12
Đặt t=x2+x+1
t(t+1)-12=t2+t-12
=(t-3)(t+4)=(x2+x+1-3)(x2+x+1+4)
=(x2+x-2)(x2+x+5)
=(x-1)(x+2)(x2+x+5)
c)(x2+8x+7)(x2+8x+15)+15
Đặt t=x2+8x+7
t(t+8)+15=t2+8t+15
=(t+3)(t+5)
=(x2+8x+7+3)(x2+8x+7+15)
=(x2+8x+10)(x2+8x+22)
d)(x+2)(x+3)(x+4)(x+5)-24
=(x2+7x+10)(x2+7x+12)-24
Đặt t=x2+7x+10
t(t+2)-24=(t-4)(t+6)
=(x2+7x+10-4)(x2+7x+10+6)
=(x2+7x+6)(x2+7x+16)
=(x+1)(x+6)(x2+7x+16)
a/ Đặt x2 + 4x + 8 = a
Thì đa thức ban đầu thành
a2 + 3ax + 2x2 = (a2 + 2ax + x2) + (ax + x2)
= (a + x)2 + x(a + x) = (a + x)(a + 2x)
Bài 1 :
a ) \(2x\left(x+1\right)+2\left(x+1\right)=\left(x+1\right)\left(2x+2\right)=2\left(x+1\right)^2\)
b ) \(y^2\left(x^2+y\right)-zx^2-zy=y^2\left(x^2+y\right)-z\left(x^2+y\right)=\left(x^2+y\right)\left(y^2-z\right)\)
c ) \(4x\left(x-2y\right)+8y\left(2y-x\right)=4x\left(x-2y\right)-8y\left(x-2y\right)=4\left(x-2y\right)^2\)
d ) \(3x\left(x+1\right)^2-5x^2\left(x+1\right)+7\left(x+1\right)=\left(x+1\right)\left(3x^2+3x-5x^2+7\right)=\left(x+1\right)\left(3x-2x^2+7\right)\)
e ) \(x^2-6xy+9y^2=\left(x-3x\right)^2\)
Bài 1 :
f ) \(x^3+6x^2y+12xy^2+8y^3=\left(x+2y\right)^3\)
g ) \(x^3-64=\left(x-4\right)\left(x^2+4x+16\right)\)
h ) \(125x^3+y^6=\left(5x+y^2\right)\left(25x^2-5xy^2+y^4\right)\)
a)
\(5x(x-2y)+2(2y-x)^2=5x(x-2y)+2(x-2y)^2\)
\(=(x-2y)[5x+2(x-2y)]=(x-2y)(7x-4y)\)
b)
\(7x(y-4)^2-(4-y)^3=7x(y-4)^2+(y-4)^3=(y-4)^2(7x+y-4)\)
c)
\((4x-8)(x^2+6)-(4x-8)(x+7)+9(8-4x)\)
\(=(4x-8)(x^2+6)-(4x-8)(x+7)-9(4x-8)\)
\(=(4x-8)[(x^2+6)-(x+7)-9]=(4x-8)(x^2-x-10)=4(x-2)(x^2-x-10)\)
d)
\(x^2-xz-9y^2+3yz=(x^2-9y^2)-(xz-3yz)\)
\(=(x-3y)(x+3y)-z(x-3y)=(x-3y)(x+3y-z)\)
e)
\(x^2(x^2-6)-x^2+9=x^4-7x^2+9=(x^4-6x^2+9)-x^2\)
\(=(x^2-3)^2-x^2=(x^2-3-x)(x^2-3+x)\)
a)
\(5x(x-2y)+2(2y-x)^2=5x(x-2y)+2(x-2y)^2\)
\(=(x-2y)[5x+2(x-2y)]=(x-2y)(7x-4y)\)
b)
\(7x(y-4)^2-(4-y)^3=7x(y-4)^2+(y-4)^3=(y-4)^2(7x+y-4)\)
c)
\((4x-8)(x^2+6)-(4x-8)(x+7)+9(8-4x)\)
\(=(4x-8)(x^2+6)-(4x-8)(x+7)-9(4x-8)\)
\(=(4x-8)[(x^2+6)-(x+7)-9]=(4x-8)(x^2-x-10)=4(x-2)(x^2-x-10)\)
d)
\(x^2-xz-9y^2+3yz=(x^2-9y^2)-(xz-3yz)\)
\(=(x-3y)(x+3y)-z(x-3y)=(x-3y)(x+3y-z)\)
e)
\(x^2(x^2-6)-x^2+9=x^4-7x^2+9=(x^4-6x^2+9)-x^2\)
\(=(x^2-3)^2-x^2=(x^2-3-x)(x^2-3+x)\)