Phân tích các đa thức sau thành nhân tử:
a) 7x3+5(x-y)2-7y3
b)8x3+27y3+4x2+9y2-6xy
c)1+x+y+z+xy+yz+zx+xyz
d)x2(y-z)+y2(z-x)+z2(x-y)
e)4x4-4x3+5x2-4x-1
g)x5+y6-x4y-xy4
1. Phân tích các đa thức sau thành nhân tử:
a) 5x2 – 10xy
b) 3x(x – y) – 6(x – y)
c) 2x(x – y) – 4y(y – x)
d) 9x2 – 9y2
e) x2 – xy – x + y
f) xy – xz – y + z
Lời giải:
a. $5x^2-10xy=5x(x-2y)$
b. $3x(x-y)-6(x-y)=(x-y)(3x-6)=3(x-y)(x-2)$
c. $2x(x-y)-4y(y-x)=2x(x-y)+4y(x-y)=(x-y)(2x+4y)=2(x-y)(x+2y)$
d. $9x^2-9y^2=9(x^2-y^2)=9(x-y)(x+y)$
e. $x^2-xy-x+y=(x^2-xy)-(x-y)=x(x-y)-(x-y)=(x-y)(x-1)$
f. $xy-xz-y+z=(xy-y)-(xz-z)=y(x-1)-z(x-1)=(x-1)(y-z)$
nhờ giải giupws em với a
1. Phân tích các đa thức sau thành nhân tử:
a) 5x2 – 10xy
b) 3x(x – y) – 6(x – y)
c) 2x(x – y) – 4y(y – x)
d) 9x2 – 9y2
e) x2 – xy – x + y
f) xy – xz – y + z
2. Phân tích các đa thức sau thành nhân tử:
a)a2 – 4b2 b) x2 – y2 + 6y - 9
c) (2a + b)2 – a2 d) 16(x – 1)2 – 25(x + y)2
e)x2 + 10x + 25 f) 25x2 – 20xy + 4y2
g)9x4 + 24x2 + 16 h) x3 – 125
i)x6 – 1 k) x3 + 15x2 + 75x + 125
3. Tìm x biết :
a) 3x2 + 8x = 0 b) 9x2 – 25 = 0 c) x3 – 16x = 0 d) x3 + x = 0.
4. Chứng minh rằng với mọi số nguyên a thì: a3 – a chia hết cho 6
Bài `1`
\(a,5x^2-10xy=5x\left(x-2y\right)\\ b,3x\left(x-y\right)-6\left(x-y\right)=\left(x-y\right)\left(3x-6\right)\\ =3\left(x-y\right)\left(x-2\right)\\ c,2x\left(x-y\right)-4y\left(y-x\right)=2x\left(x-y\right)+4y\left(x-y\right)\\ =\left(x-y\right)\left(2x+4y\right)=2\left(x-y\right)\left(x+2y\right)\\ d,9x^2-9y^2=\left(3x\right)^2-\left(3y\right)^2=\left(3x-3y\right)\left(3x+3y\right)\\ f,xy-xz-y+z=\left(xy-xz\right)-\left(y-z\right)\\ =x\left(y-z\right)-\left(y-z\right)=\left(y-z\right)\left(x-1\right)\)
Bài `3`
\(a,3x^2+8x=0\\ \Leftrightarrow x\left(3x+8\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\3x+8=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\3x=-8\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{8}{3}\end{matrix}\right.\)
\(b,9x^2-25=0\\ \Leftrightarrow\left(3x\right)^2-5^2=0\\ \Leftrightarrow\left(3x-5\right)\left(3x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}3x-5=0\\3x+5=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}3x=5\\3x=-5\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{5}{3}\\x=-\dfrac{5}{3}\end{matrix}\right.\)
\(c,x^3-16x=0\\ \Leftrightarrow x\left(x^2-16\right)=0\\ \Leftrightarrow x\left(x-4\right)\left(x+4\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x-4=0\\x+4=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\\x=-4\end{matrix}\right.\)
\(d,x^3+x=0\\ \Leftrightarrow x\left(x^2+1\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x^2+1\in\varnothing\\x=0\end{matrix}\right.\Rightarrow x=0\)
MỌI NGƯỜI GIÚP MK VỚI!!!
Phân tích đa thức sau thành nhân tử:
A=xyz+(x+y+z)-1-( xy+yz+zx)
B=x2y+y2z+z2x+xy2+yz2+zx2+3xyz
C=yz(y+z)+zx(z-x)-xy(x+y)
D=(x+2)(x+3)(x+4)(x+5)-24
bài 1: Phân tích đa thức thành nhân tử
a, (xy-1)2+ (x+y)2
b, a2+2a2+2a+1
c, (1+2a).(1-2a)-a.(a+2).(a-2)
d, a2+b2-a2b2+ab-a-b
e, xy.(x+y)-yz.(y+z)+xz(x-z)
f, xyz-(xy+yz+zx)+(x+y+z)-1
giúp em với ạ ! em đang cần gấp
\(a,=\left(xy-1-x-y\right)\left(xy-1+x+y\right)\\ b,Sửa:a^3+2a^2+2a+1\\ =a^3+a^2+a^2+a+a+1=\left(a+1\right)\left(a^2+a+1\right)\\ c,=1-4a^2-a\left(a^2-4\right)=1-4a^2-a^3+4a\\ =\left(1-a\right)\left(1+a+a^2\right)+4a\left(1-a\right)\\ =\left(1-a\right)\left(1+5a+a^2\right)\\ d,=\left(a^2-a^2b^2\right)+\left(b^2-b\right)+\left(ab-a\right)\\ =a^2\left(1-b\right)\left(1+b\right)+b\left(b-1\right)+a\left(b-1\right)\\ =\left(b-1\right)\left(-a^2-ab+b+a\right)\\ =\left(b-1\right)\left(b-1\right)\left(a+b\right)\left(1-a\right)\)
\(e,=x^2y+xy^2-yz\left(y+z\right)+x^2z-xz^2\\ =\left(x^2y+x^2z\right)+\left(xy^2-xz^2\right)-yz\left(y+z\right)\\ =x^2\left(y+z\right)+x\left(y-z\right)\left(y+z\right)-yz\left(y+z\right)\\ =\left(y+z\right)\left(x^2+xy-xz-yz\right)\\ =\left(y+z\right)\left(x+y\right)\left(x-z\right)\)
\(f,=xyz-xy-yz-xz+x+y+z-1\\ =xy\left(z-1\right)-y\left(z-1\right)-x\left(z-1\right)+\left(x-1\right)\\ =\left(z-1\right)\left(xy-y-x+1\right)=\left(z-1\right)\left(x-1\right)\left(y-1\right)\)
phân tích a)(x-y)3+(y-z)3+(z-x)3
b)x.(y2-z2)+y.(z2-x2)+z.(x2-y2)
c)xy.(x-y)-xz.(x+z)-yz.(zx-y+z)
d)x.(y+z)2+y.(z-x)2+z.(x+y)2-4xyz
a)(x-y)3+(y-z)3+(z-x)3
=3(x-y+y-z+z-x)=3
b)nhân vào là rồi đối trừ là hết luôn ( nhưng là mũ 2 hay nhân 2 v mk là theo nhân 2 nhé]
Phân tích đa thức thành nhân tử
A ) xy(z+y)+yz(y+z)+zx(z+x)
B )xy(x+y)-yz(y+z)-zx(z-x)
A ) xy(z+y)+yz(y+z)+zx(z+x)
=y.[x(z+y)+z(y+z)]+zx(z+x)
=y.(xz+xy+zy+z2)+zx(z+x)
=y.(xz+z2+xy+zy)+zx(z+x)
=y.[z.(z+x)+y.(z+x)]+zx(z+x)
=y.(z+x)(z+y)+zx(z+x)
=(z+x)[y(z+y)+zx]
=(z+x)(yz+y2+zx)
B )xy(x+y)-yz(y+z)-zx(z-x)
=y.[x(x+y)-z(y+z)]-zx(z-x)
=y.(x2+xy-zy-z2)-zx(z-x)
=y.(x2-z2+xy-zy)-zx(z-x)
=y.[(x+z)(x-z)+y.(x-z)]-zx(z-x)
=y.(x-z)(x+z+y)+zx(x-z)
=(x-z)[y(x+z+y)+zx]
=(x-z)(yx+yz+y2+zx)
=(x-z)(yx+zx+yz+y2)
=(x-z)[x.(y+z)+y.(y+z)]
=(x-z)(y+z)(x+y)
b. \(\text{ xy(x+y)-yz(y+z)-xz(z-x) =xy(x+y+z-z)+yz(y+z)+xz(x-z) =xy(x-z)+xy(y+z)+yz(y+z)+xz(x-z) =(x+y)(y+z)(x-z) }\)
phân tích đa thức thành nhân tử
a/ x2 - 4x + 4 – y2 e/ 25x2 - 4y2
b/ 4x4 + 8x3 + 4x2 f/ x2 + 7x + 12
c/ x3y2 – 2x2y3 + xy4 i/ x2 - 5x - 14
d/ x2 - y2 – 7x + 7y
giúp mình với mình đang cần gấp ạ
\(a,=\left(x-2\right)^2-y^2=\left(x-y-2\right)\left(x+y-2\right)\\ b,=4x^2\left(x^2+2x+1\right)=4x^2\left(x+1\right)^2\\ c,=xy^2\left(x^2-2xy+y^2\right)=xy^2\left(x-y\right)^2\\ d,=\left(x-y\right)\left(x+y\right)-7\left(x-y\right)=\left(x-y\right)\left(x+y-7\right)\\ e,=\left(5x-2y\right)\left(5x+2y\right)\\ f,=x^2+3x+4x+12=\left(x+3\right)\left(x+4\right)\\ i,=x^2+2x-7x-14=\left(x+2\right)\left(x-7\right)\)
Phân tích đa thức thành nhân tử:
a) m x 2 + my - n x 2 - ny; b) mz - 2z - m 2 + 2m;
c) x 2 y 2 + y 3 + z x 2 + yz; d) 2x2 + 4mx + x + 2m.
e) x 4 - 9 x 3 + x 2 - 9x; g) 3 x 2 -2 ( x - y ) 2 - 3 y 2 .
h*) xy(x + y) + yz (y + z) + xz(x + z) + 2xyz.
1.Đa thức 4x(2y-z) +7y(2y-z) được phân tích thành nhân tử là :
A .(2y+z)(4x+7y)
B.(2y-z)(4x-7y)
C.(2y+z)(4x-7y)
D. (2y-z)(4x+7y)
2 Phân tích đa thức x2+3x+xy+3y thành nhân tử ta được :
A. (x+3)(y+3)
B. (x-y)(x+3)
C. (x+3)(x+y)
D. Cả 3 đều sai
1). x2y2(y-x)+y2z2(z-y)-z2x2(z-x)
2)xyz-(xy+yz+xz)+(x+y+z)-1
3)yz(y+z)+xz(z-x)-xy(x+y)
4)2a2b+4ab2-a2c+ac2-4b2c+2bc2-4abc
5)y(x-2z)2+8xyz+x(y-2z)2-2z(x+y)2
6)8x3(y+z)-y3(z+2x)-z3(2x-y)
7) (x2+y2)3+(z2-x2)3-(y2+z2)3