CỨU TỚ VỚIII !!! HELP ME !!
phân tích các đa thức sau thành nhân tử
A) (x+1)^4 (x-1)^4
B) ( x -y +4)^2 - ( 2x + 3y -1)^2
C) -x^4/4 + 2x^2y^3 - 4y^6
D) y^9 - 9x^2y^6 + 27 x^4y^3 -27x^6
Phân tích các đa thức sau đây thành nhân tử
a, 36x^2 - ( 3x -2 ) ^2
b, 16(4x+5)^5 - 25 (2x+2)^2
c, ( x - y + 4 )^2
d, (x+1)^4 - (x-1)^4
e, 16x^2 - 24xy + 9y^2
f, -x^4/4 + 2x^2y^3 - 4y^6
g , 64x^3 +1
h, x^3y^6z^9 - 125
k, 27x^6 - 8x^3
I , x^6 - y^6
m, 27x^3 - 54x^2y + 36xy^2 - 8y^3
n, y^9 - 9x^2y^6 + 27x^4y^3 - 27x^6
làm ơn giải chi tiết giúp mik vs ạ , cảm ơn
a: =(6x)^2-(3x-2)^2
=(6x-3x+2)(6x+3x-2)
=(9x-2)(3x+2)
d: \(=\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\)
\(=4x\cdot\left[x^2+2x+1+x^2-2x+1\right]\)
=8x(x^2+1)
e: =(4x)^2-2*4x*3y+(3y)^2
=(4x-3y)^2
f: \(=-\left(\dfrac{1}{4}x^4-2\cdot\dfrac{1}{2}x^2\cdot2y^3+4y^6\right)\)
\(=-\left(\dfrac{1}{2}x^2-2y^3\right)^2\)
g: =(4x)^3+1^3
=(4x+1)(16x^2-4x+1)
k: =x^3(27x^3-8)
=x^3(3x-2)(9x^2+6x+4)
l: =(x^3-y^3)(x^3+y^3)
=(x-y)(x+y)(x^2-xy+y^2)(x^2+xy+y^2)
Bài 1: Phân tích đa thức sau :
a)2x(xy+y^2-3)
b)(x-y)(2x+y)
c)(x-2y)^2
d)(2x-y)(y+2x)
bài 2: Phân tích các đơn thức thành nhân tử
a)3x^2-3xy
b)x^2-4y^2
c)3x-3y+xy-y^2
d)x^2-1+2y-y^2
Bài 3: Tìm x biết:
a)3x^2-6x=0
b)Tìm x,y thuộc z biết: x^2+4y^2-2xy=4
Bài 2:
a: \(3x^2-3xy=3x\left(x-y\right)\)
b: \(x^2-4y^2=\left(x-2y\right)\left(x+2y\right)\)
c: \(3x-3y+xy-y^2=\left(x-y\right)\left(3+y\right)\)
d: \(x^2-y^2+2y-1=\left(x-y+1\right)\left(x+y-1\right)\)
Phân tích đa thức 8𝑥 3 -1 thành nhân tử
A.(2𝑥 − 1)(4𝑥 2+2x+1)
B.(2𝑥 + 1)(4𝑥 2+2x+1)
C.(2𝑥 − 1)(4𝑥 2 - 2x+1)
D.(2𝑥 − 1)(4𝑥 2+4x+1)
Câu 17 Phân tích đa thức 5x2 -4x +10xy-8y thành nhân tử
A..(5x-4)(x-2y)
B. (x+2y)(5x-4)
C.(5x-2y)(x+4y)
D.(5x+4)(x-2y)
Câu 18 Phân tích đa thức 8x3 + 12x2y + 6xy2 + y3 thành nhân tử :
A. (2x + y)3
B.(2x - y)3
C. (2x + y3 ) 3
D. (2x3 + y)3
Câu 19 Tìm x, biết (x + 2) . ( x – 1 ) – x 2 = –1
A. x = –2 4
B. x = 2
C. x = 1
D. x = –1
Câu 20 Tìm x biết x . ( x – 3) = x2 + 6
A. x = 2
B. x = –2
C. x = 4
D. x = 6
Câu 21 Tìm x biết : (𝑥 + 3)(𝑥 − 3) − 𝑥(𝑥 − 3) =0
A. x = 3.
B. x= -3
C. x=1
D. x=0
\(16,A\\ 17,C\\ 18,A\\ 19,C\\ 20,A\\ 21,A\)
Phân tích đa thức thành nhân tử
a.\(16x^3+0,25yz^3\)
b.\(x^4-4x^3+4x^2\)
c.\(x^3+x^2y-xy^2-y^3\)
d.\(x^3+x^2+x+1\)
e.\(x^4-x^2+2x-1\)
f.\(2x^2-18\)
g.\(x^2+8x+7\)
h.\(x^4y^4+4\)
i.\(x^4+4y^4\)
k.\(x^2-2x-15\)
a: \(16x^3+0,25yz^3\)
\(=0,25\cdot x^3\cdot64+0,25\cdot yz^3\)
\(=0,25\left(64x^3+yz^3\right)\)
b: \(x^4-4x^3+4x^2\)
\(=x^2\cdot x^2-x^2\cdot4x+x^2\cdot4\)
\(=x^2\left(x^2-4x+4\right)=x^2\left(x-2\right)^2\)
c: \(x^3+x^2y-xy^2-y^3\)
\(=x^2\left(x+y\right)-y^2\left(x+y\right)\)
\(=\left(x+y\right)\left(x^2-y^2\right)\)
\(=\left(x+y\right)\left(x-y\right)\left(x+y\right)\)
\(=\left(x-y\right)\cdot\left(x+y\right)^2\)
d: \(x^3+x^2+x+1\)
\(=x^2\left(x+1\right)+\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2+1\right)\)
e: \(x^4-x^2+2x-1\)
\(=x^4-\left(x^2-2x+1\right)\)
\(=x^4-\left(x-1\right)^2\)
\(=\left(x^2-x+1\right)\left(x^2+x-1\right)\)
f: \(2x^2-18\)
\(=2\cdot x^2-2\cdot9\)
\(=2\left(x^2-9\right)=2\left(x-3\right)\left(x+3\right)\)
g: \(x^2+8x+7\)
\(=x^2+x+7x+7\)
\(=x\left(x+1\right)+7\cdot\left(x+1\right)=\left(x+1\right)\left(x+7\right)\)
h: \(x^4y^4+4\)
\(=x^4y^4+4x^2y^2+4-4x^2y^2\)
\(=\left(x^2y^2+2\right)^2-\left(2xy\right)^2\)
\(=\left(x^2y^2+2-2xy\right)\left(x^2y^2+2+2xy\right)\)
i: \(x^4+4y^4\)
\(=x^4+4x^2y^2+4y^4-4x^2y^2\)
\(=\left(x^2+2y^2\right)^2-\left(2xy\right)^2\)
\(=\left(x^2-2xy+2y^2\right)\left(x^2+2xy+2y^2\right)\)
k: \(x^2-2x-15\)
\(=x^2-5x+3x-15\)
\(=x\left(x-5\right)+3\left(x-5\right)=\left(x-5\right)\left(x+3\right)\)
1.Tính \(\dfrac{x}{x+2}-\dfrac{x}{x-2}\)
2.Phân tích đa thức thành nhân tử
1)\(\left(x^2y^2-8\right)-1\)
2)\(x^3y-2x^2y+xy-xy^3\)
3)\(x^3-2x^2y+xy^2\)
4)\(x^2+2x-y^2+1\)
5)\(x^2+2x-4y^2+1\)
6)\(x^2-6x-y^2+9\)
bài 1: ĐKXĐ: \(x\notin\left\{2;-2\right\}\)
\(\dfrac{x}{x+2}-\dfrac{x}{x-2}\)
\(=\dfrac{x\left(x-2\right)-x\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}\)
\(=\dfrac{x^2-2x-x^2-2x}{\left(x-2\right)\left(x+2\right)}=-\dfrac{4x}{x^2-4}\)
Bài 2:
1: \(x^2y^2-8-1\)
\(=x^2y^2-9\)
\(=\left(xy-3\right)\left(xy+3\right)\)
2: \(x^3y-2x^2y+xy-xy^3\)
\(=xy\cdot x^2-xy\cdot2x+xy\cdot1-xy\cdot y^2\)
\(=xy\left(x^2-2x+1-y^2\right)\)
\(=xy\left[\left(x-1\right)^2-y^2\right]\)
\(=xy\left(x-1-y\right)\left(x-1+y\right)\)
3: \(x^3-2x^2y+xy^2\)
\(=x\cdot x^2-x\cdot2xy+x\cdot y^2\)
\(=x\left(x^2-2xy+y^2\right)=x\left(x-y\right)^2\)
4: \(x^2+2x-y^2+1\)
\(=\left(x^2+2x+1\right)-y^2\)
\(=\left(x+1\right)^2-y^2\)
\(=\left(x+1+y\right)\left(x+1-y\right)\)
5: \(x^2+2x-4y^2+1\)
\(=\left(x^2+2x+1\right)-4y^2\)
\(=\left(x+1\right)^2-4y^2\)
\(=\left(x+1-2y\right)\left(x+1+2y\right)\)
6: \(x^2-6x-y^2+9\)
\(=\left(x^2-6x+9\right)-y^2\)
\(=\left(x-3\right)^2-y^2=\left(x-3-y\right)\left(x-3+y\right)\)
viết các đa thức sau ra tích hoặc lũy thừa :
1/ x^2 +4xy+4y^2
2) -x^3 + 9x^2 - 27x + 27
3) 8x^6 + 36 x^4y + 54x^2y^2 + 27y^3
4) x^3 - 6x^2y + 12xy^2 - 8y^3
5) x^2 + 4y^2 +1 - 4xy -2x+4y
6) x^2+y^2 +4 + 2xy + 4x + 4y
ai nhanh mk tik cho nha , cám ơn
1/ x^2 +4xy +4y^2 = (x +2y)^2
2/ -x^3 +9x^2 -27x+27= - (x^3 -9x^2+27x-27) = - (x-3)^3
3/ 8x^6 +36x^4y+54^2y^2+27y^3 = (2x^2+3y)^3
4/ x^3 - 6x^2y+12xy^2 -8y^3= (x-2y)^3
1) x2 + 4xy + 4y2 = ( x + 2y )2
2) - x3 + 9x2 - 27x + 27 = ( 3 - x )2
3) 8x6 + 36x4y + 54x2y2 + 27y3 = ( 2x2 + 3y )3
4) x3 - 6x2y + 12xy2 - 8y3 = ( x - 2y )3
5) x2 + 4y2 +1 - 4xy - 2x + 4y = ( x2 - 2y - 1 )2
6) x2 + y2 + 4 + 2xy + 4x + 4y = ( x + y + 2 )2
Phân tích các đa thức sau thành nhân tử:
1, x^2-2x-4y^2-4y
2, x^4+2x^3-4x-4
3, 3x^2-3y^2-2.(x-y)^2
4, x^2-y^2-2x-2y
Giúp tớ với ạ:33
\(1,\)
\(x^2-2x-4y^2-4y\)
\(=\left(x-2y\right)\left(x+2y\right)-2\left(x+2y\right)\)
\(=\left(x+2y\right)\left(x-2y-2\right)\)
\(2,\)
\(x^4+2x^3-4x-4\)
\(=\left(x^2-2\right)\left(x^2+2\right)+2x\left(x^2-2\right)\)
\(=\left(x^2-2\right)\left(x^2+2x+2\right)\)
\(3,\)
\(3x^2-3y^2-2\left(x-y\right)^2\)
\(=3\left(x^2-y^2\right)-2\left(x-y\right)^2\)
\(=3\left(x-y\right)\left(x+y\right)-2\left(x-y\right)\)
\(=\left(x-y\right)[3\left(x+y\right)-2\left(x-y\right)]\)
\(=\left(x-y\right)\left(3x+3y-2x+2y\right)\)
\(=\left(x-y\right)\left(x+5y\right)\)
\(4,\)
\(x^2-y^2-2x+2y\)
\(=x^2-y^2-2x+2y\)
\(=\left(x-y\right)\left(x+y\right)-2\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-2\right)\)
Phân tích đa thức thành nhân tử:
a. x²-y²-2x-2y
b. 3x²-3y²-2(x-y)²
c. x²-2x-4y²-4y
d. x²-2x-4y²-4y
e. x³-4x²-9x+36
f. a mũ 6-a⁴+2a³+2a²
g. (a+b)³-(a-b)³
h. x³+2x²+2x+1
i. x⁴+2x³-4x-4
j. x³-4x²+12x-27
k. x⁴-2x³+2x-1
a)=x2-2x+1-y2-2y-1
=(x-1)2-(y+1)2
=(x-1+y+1)(x-1-y-1)=(x+y)(x-y-2)
bài 1: phân tích các đa thức thành nhân tử:
a)x(3-4x)+5(3-4x)
b)2y(5y-6)-4(6-5y)
c)27(x-2)^3-3x(2-x)^2
d)6y(x^2-y^2)-8y(x+y)^2
bài 2:
a)2x^2-xy+2xz-yz
b)x^2-x+2y-4y^2
c)y^2+10y-9z^2+25
d) (x+2y)^3-x^2+4y^2
giúp mik nhé mik cần gấp ạ
2:
a: \(=\left(2x^2-xy\right)+\left(2xz-yz\right)\)
\(=x\left(2x-y\right)+z\left(x-2y\right)=\left(x-2y\right)\left(x+z\right)\)
b: \(=\left(x^2-4y^2\right)-\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x+2y\right)-\left(x-2y\right)\)
\(=\left(x-2y\right)\left(x+2y-1\right)\)
c: \(=\left(y^2+10y+25\right)-9z^2\)
\(=\left(y+5\right)^2-\left(3z\right)^2\)
\(=\left(y+5+3z\right)\left(y+5-3z\right)\)
d: \(=\left(x+2y\right)^3-\left(x-2y\right)\left(x+2y\right)\)
\(=\left(x+2y\right)\left[\left(x+2y\right)^2-\left(x-2y\right)\right]\)
\(=\left(x+2y\right)\left(x^2+4xy+4y^2-x+2y\right)\)
1:
a: \(x\left(3-4x\right)+5\left(3-4x\right)=\left(3-4x\right)\left(x+5\right)\)
b: \(2y\left(5y-6\right)-4\left(6-5y\right)\)
\(=2y\left(5y-6\right)+4\left(5y-6\right)\)
\(=2\left(5y-6\right)\left(y+2\right)\)
c: \(=27\left(x-2\right)^3-3x\left(x-2\right)^2\)
\(=3\left(x-2\right)^2\cdot\left[9\left(x-2\right)-x\right]\)
\(=3\left(x-2\right)^2\left(8x-18\right)=6\left(x-2\right)^2\cdot\left(4x-9\right)\)
d: \(=6y\left(x-y\right)\left(x+y\right)-8y\left(x+y\right)^2\)
\(=2y\left(x+y\right)\left[3\left(x-y\right)-4\left(x+y\right)\right]\)
\(=2y\left(x+y\right)\left(3x-3y-4x-4y\right)\)
\(=2y\left(x+y\right)\left(-x-7y\right)\)
Bài 1
a) x(3 - 4x) + 5(3 - 4x)
= (3 - 4x)(x + 5)
b) 2y(5y - 6) - 4(6- 5y)
= 2y(5y - 6) + 4(5y - 6)
= (5y - 6)(2y + 4)
= 2(5y - 6)(y + 2)
c) 27(x - 2)³ - 3x(2 - x)²
= 27(x - 2)³ - 3x(x - 2)²
= 3(x - 2)²[9(x - 2) - x]
= 3(x - 2)²(9x - 18 - x)
= 3(x - 2)²(8x - 18)
= 6(x - 2)²(4x - 9)
d) 6y(x² - y²) - 8y(x + y)²
= 6y(x - y)(x + y) - 8y(x + y)²
= 2y(x + y)[3(x - y) - 4(x + y)]
= 2y(x + y)(3x - 3y - 4x - 4y)
= 2y(x + y)(-x - 7y)
= -2y(x + y)(x + 7y)