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a) (x+2) \(\left(x^2-2x+4\right)\)
b) (3 - 2y) \(\left(9+6y+4y^2\right)\)
d) (4x - y) \(\left(16x^2+4xy+y^2\right)\)
bạn giải chi tiết hộ mình với nha.mk sắp phải nộp bài r. huhuhuhu
a)
\(x^5+x^3-x^2-1\)
\(=x^3\left(x^2+1\right)-\left(x^2+1\right)\)
\(=\left(x^2+1\right)\left(x^3-1\right)\)
\(=\left(x^2+1\right)\left(x-1\right)\left(x^2+x+1\right)\)
b)
\(x^2-3x^3-x+3\)
\(=x\left(x-1\right)-3\left(x^3-1\right)\)
\(=x\left(x-1\right)-3\left(x-1\right)\left(x^2+x+1\right)\)
\(=\left(x-1\right)\left(x-3x^2-3x-3\right)\)
\(=\left(x-1\right)\left(-3x^2-2x-3\right)\)
c)
\(x^2-6x+8\)
\(=x^2-2.x.3+9-1\)
\(=\left(x-3\right)^2-1\)
\(=\left(x-3-1\right)\left(x-3+1\right)\)
\(=\left(x-4\right)\left(x-2\right)\)
d)
\(4x^4-4x^2y^2-8y^4\)
\(=\left(2x^2\right)^2-2.\left(2x^2\right)y^2+y^2-9y^4\)
\(=\left(2x^2-y\right)^2-\left(3y^2\right)^2\)
\(=\left(2x^2-y-3y^2\right)\left(2x^2-y+3y^2\right)\)
a,nhóm x*5 với x*3,x*2 và 1: (x*5+ x*3) - (x*2+1) =x*3.(x*2+1)-(x*2+1) =....., câu b nhóm x*2 và -3x*3,x và 3, câu c bang (x-3)*2-1 =..., câu d đat 4 ra.
a) \(x^5+x^3-x^2-1=x^3\left(x^2+1\right)-\left(x^2+1\right)=\left(x^3-1\right)\left(x^2+1\right)\)
b) \(x^2-3x^3-x+3=x\left(x-1\right)-3\left(x^3-1\right)=x\left(x-1\right)-3\left(x-1\right)\left(x^2+x+1\right)=\left(x-1\right)\left[\left(x-3\right)-\left(x^2+x+1\right)\right]=\left(x-1\right)\left(-x^2-4\right)\)c) \(x^2-6x+8=x^2-6x+9-1=\left(x-3\right)^2-1=\left(x-2\right)\left(x-4\right)\)
d) \(4x^4+4x^2y^2-8y^4=4x^4+4x^2y^2+y^4-9y^4=\left(2x^2+y^2\right)^2-9y^4=\left(2x^2+4y^2\right)\left(2x^2-2y^2\right)=2\left(x^2+2y^2\right)2\left(x^2-y^2\right)=4\left(x^2+2y^2\right)\left(x+y\right)\left(x-y\right)\)
a) \(x^3+6x^2+12x+8\)
\(=\left(x+2\right)^3\)
b) \(x^3-3x^2+3x-1\)
\(=\left(x-1\right)^3\)
c) \(1-9x+27x^2-27x^3\)
\(=-\left(27x^3-27x^2+9x-1\right)\)
\(=-\left(3x-1\right)^3\)
\(a,x^3+8y^3=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)
\(b,a^6-b^3=\left(a^2-b\right)\left(a^4+a^2b+b^2\right)\)
\(c,8y^3-125=\left(2y-5\right)\left(4y^2+10y+25\right)\)
\(d,8z^3+27=\left(2z+3\right)\left(4z^2-6z+9\right)\)
\(a)x^3+8y^3=x^3+\left(2y\right)^3=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)
\(b)a^6-b^3=\left(a^3-b^3\right)\left(a^3+b^3\right)\)
\(c)8y^3-125=\left(2y\right)^3-5^3=\left(2y-5\right)\left(4y^2+10y+25\right)\)
\(d)8z^3+27=\left(2z\right)^3+3^3=\left(2x+3\right)\left(4z^2-6z+9\right)\)
Bài 1 : Phân tích các đa thức sau thành nhân tử :
a) 8x3 - 64
=(2x)3 + 43
=(2x+4)(4x2 - 8x + 16)
c) 125x3 + 1
=5x3 + 13
=(5x+1)(25x2 +5x+1)
d) 8x3 - 27
=(2x)3 - 33
=(2x - 3)(2x2 + 6x + 9)
e) 1 + 8x6y3
=1 + (2x2y)3
=(1 + 2x2y)(4x4y2 -2x2y + 1)
f) 125x3 + 27y3
=(5x)3 + (3y3)
=(5x + 3y)(25x2 - 15xy + 9y2)
Bài 1
a) \(8x^3-64\)
\(=\left(2x\right)^3-4^3\)
\(=\left(2x-4\right)\left(4x^2+8x+16\right)\)
c) \(125x^3+1\)
\(=\left(5x\right)^3+1^3\)
\(=\left(5x+1\right)\left(25x^2-5x+1\right)\)
d) \(8x^3-27\)
\(=\left(2x\right)^3-3^3\)
\(=\left(2x-3\right)\left(4x^2+6x+9\right)\)
e) \(1+8x^6x^3\)
\(=1^3+\left(2x^2y\right)^3\)
\(=\left(1+2x^2y\right)\left(1-2x^2y+4x^4y^2\right)\)
f) \(125x^3+27y^3\)
\(=\left(5x\right)^3+\left(3y\right)^3\)
\(=\left(5x+3y\right)\left(25x^2-15xy+9x^2\right)\)
\(a,\left(a^3-b^3\right)+\left(a-b\right)^2\)
\(=\left(a-b\right)\left(a^2+ab+b^2\right)+\left(a-b\right)^2\)
\(=\left(a-b\right)\left(a^2+ab+b^2+a-b\right)\)
\(b,\left(x^2+1\right)^2-4x^2\)
\(=x^4+2x^2+1-4x^2\)
\(=x^4-2x^2+1\)
\(\left(x^2-1\right)^2\)
\(c\left(y^3+8\right)+\left(y^2-4\right)\)
\(=\left(y+2\right)\left(y^2-8y+4\right)+\left(y-2\right)\left(y+2\right)\)
\(=\left(y+2\right)\left(y^2-8y+4+y-2\right)\)
\(=\left(y+2\right)\left(y^2-7y+2\right)\)
a) ( a3 - b3) + ( a - b)2
= (a-b) (a2 + ab + b2 ) + (a-b)2
= (a-b) (a2 + ab + b2 +a -b )
hok tốt
a) 1 - 2y + y2
= (1-y)2
b) ( x + 1 )2 - 25
=( x + 1 )2 - 52
=(x+1+5)(x+1-5)
a) x^3 + 8 = x^3 + 2^3 = (x+2)(x^2-2x+2)
b) 27-8y^3 =3^3-(2y)^3=(3-2y)(3^2+2*3Y+8y^3)
c) y^6+1= (y^2)^3+1^3 = (y^2+1)(Y^6+ y^2+ 1)
bài này áp dụng hằng đẳng thức đáng nhớ bạn nhé