Phân tích đa thức thành nhân tử :
a. \(\dfrac{1}{2}x^2-2y^2\)
b. \(\dfrac{1}{3}xy+x^2z+xz\)
c. \(18x^3-\dfrac{8}{25}x\)
d. \(\dfrac{2}{5}x^2+5x^3+x^2y\)
e. \(\dfrac{1}{2}\left(x^2+y^2\right)^2-2x^2y^2\)
f. \(27x^3-\dfrac{1}{8}y^3\)
Phân tích đa thức thành nhân tử :
a. \(\dfrac{1}{2}x^2-2y^2\)
b. \(\dfrac{1}{3}xy+x^2z+xz\)
c. \(18x^3-\dfrac{8}{25}x\)
d. \(\dfrac{2}{5}x^2+5x^3+x^2y\)
e. \(\dfrac{1}{2}\left(x^2+y^2\right)^2-2x^2y^2\)
f. \(27x^3-\dfrac{1}{8}y^3\)
g. \(\dfrac{1}{2}x^2+\dfrac{1}{4}x+\dfrac{1}{32}\)
\(a,=2\left(\dfrac{1}{4}x^2-y^2\right)=2\left(\dfrac{1}{2}x-y\right)\left(\dfrac{1}{2}x+y\right)\\ b,=\dfrac{1}{3}x\left(y+3xz+3z\right)\\ c,=2x\left(9x^2-\dfrac{4}{25}\right)=2x\left(3x-\dfrac{2}{5}\right)\left(3x+\dfrac{2}{5}\right)\)
\(d,=x^2\left(\dfrac{2}{5}+5x+y\right)\\ e,=\dfrac{1}{2}\left[\left(x^2+y^2\right)^2-4x^2y^2\right]\\ =\dfrac{1}{2}\left(x^2-2xy+y^2\right)\left(x^2+2xy+y^2\right)\\ =\dfrac{1}{2}\left(x-y\right)^2\left(x+y\right)^2\\ f,=\left(3x-\dfrac{1}{2}y\right)\left(9x^2+\dfrac{3}{2}xy+\dfrac{1}{4}y^2\right)\\ g,=\dfrac{1}{2}\left(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\right)=\dfrac{1}{2}\left(x+\dfrac{1}{4}\right)^2\)
Phân tích đa thức thành nhân tử :
a. \(\dfrac{1}{2}x^2-2y^2\)
b. \(\dfrac{1}{3}xy+x^2z+xz\)
c. \(18x^3-\dfrac{8}{25}x\)
d. \(\dfrac{2}{5}x^2+5x^3+x^2y\)
Lời giải:
a.
$=\frac{1}{2}(x^2-4y^2)=\frac{1}{2}[x^2-(2y)^2]=\frac{1}{2}(x-2y)(x+2y)$
b.
$=\frac{1}{3}x(y+3xz+3z)$
c.
$=\frac{2}{25}x(225x^2-4)=\frac{2}{25}(15x-2)(15x+2)$
d.
$=\frac{1}{5}x^2(2+25x+5y)$
Phân tích đa thức thành nhân tử
a. \(\dfrac{1}{2}\left(x^2+y^2\right)^2-2x^2y^2\)
b. \(27x^3-\dfrac{1}{8}y^3\)
c. \(\dfrac{1}{2}x^2+\dfrac{1}{4}x+\dfrac{1}{32}\)
\(a,=\dfrac{1}{2}\left[\left(x^2+y^2\right)^2-4x^2y^2\right]\\ =\dfrac{1}{2}\left(x^2-2xy+y^2\right)\left(x^2+2xy+y^2\right)\\ =\dfrac{1}{2}\left(x-y\right)^2\left(x+y\right)^2\\ b,=\left(3x-\dfrac{1}{2}y\right)\left(9x^2+\dfrac{3}{2}xy+\dfrac{1}{4}y^2\right)\\ c,=\dfrac{1}{2}\left(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\right)=\dfrac{1}{2}\left(x+\dfrac{1}{4}\right)^2\)
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: \(x^2-6x-y^2+9\)
\(=\left(x^2-6x+9\right)-y^2\)
\(=\left(x-3\right)^2-y^2=\left(x-3-y\right)\left(x-3+y\right)\)
Phân tích đa thức \(\dfrac{2}{5}x^2+5x^3+x^2y\) thành nhân tử
a. \(x^2\left(\dfrac{2}{5}+5x+y\right)\)
b. \(\dfrac{1}{5}x^2\left(2+25x+5y\right)\)
Cách phân tích nào đúng a hay b và GIẢI THÍCH VÌ SAO?
A. Cách B sai vì 5 : 2/5 thì ko thể nào = 25 đc.
phân tích đa thức \(\dfrac{1}{2}x^2-2y^2\) thành nhân tử
a. \(\dfrac{1}{2}x^2-2y^2=\dfrac{1}{2}\left(x^2-4y^2\right)=\dfrac{1}{2}\left(x-2y\right)\left(x+2y\right)\)
b. \(\dfrac{1}{2}x^2-2y^2=2\left(\dfrac{1}{4}x^2-y^2\right)=2\left(\dfrac{1}{2}x-y\right)\left(\dfrac{1}{2}x+y\right)\)
Cách phân tích nào đúng, a hay b ?
phân tích đa thức \(\dfrac{1}{2}x^2-2y^2\) thành nhân tử
a. \(\dfrac{1}{2}x^2-2y^2=\dfrac{1}{2}\left(x^2-4y^2\right)=\dfrac{1}{2}\left(x-2y\right)\left(x+2y\right)\)
b. \(\dfrac{1}{2}x^2-2y^2=2\left(\dfrac{1}{4}x^2-y^2\right)=2\left(\dfrac{1}{2}x-y\right)\left(\dfrac{1}{2}x+y\right)\)
Cách phân tích nào đúng, a hay b ?
Thực hiện phép tính:
a) \(\dfrac{2}{5}xy\left(x^2y-5x+10y\right)\)
b) \(\left(x^2-1\right)\left(x^2+2x+y\right)\)
c) \(\left(x+3y\right)^2\)
d) \(\left(4x-y\right)^3\)
e) \(\left(x^2-2y\right)\left(x^2+2y\right)\)
g) \(18x^4y^2z:10x^4y\)
h) \(\left(x^3y^3+\dfrac{1}{2}x^2y^3-x^3y^2\right):\dfrac{1}{3}x^2y^2\)
i) \(\left(6x^3-7x^2-x+2\right):\left(2x+1\right)\)
k) \(\dfrac{5x-1}{3x^2y}+\dfrac{x+1}{3x^2y}\)
l) \(\dfrac{3x+1}{x^2-3x+1}+\dfrac{x^2-6x}{x^2-3x+1}\)
m) \(\dfrac{2x+3}{10x-4}+\dfrac{5-3x}{4-10x}\)
n) \(\dfrac{x}{x^2+2x+1}+\dfrac{3}{5x^2-5}\)
o) \(\dfrac{x^2+2}{x^3-1}+\dfrac{2}{x^2+x+1}+\dfrac{1}{1-x}\)
p) \(\dfrac{4x+2}{15x^3y}\dfrac{5y-3}{9x^2y}+\dfrac{x+1}{5xy^3}\)
q) \(\dfrac{2x-7}{10x-4}-\dfrac{3x+5}{4-10x}\)
r) \(\dfrac{3}{2x+6}-\dfrac{x-6}{2x^2+6x}\)
x) \(\dfrac{4y^2}{11x^4}.\left(-\dfrac{3x^2}{8y}\right)\)
y) \(\dfrac{x^2-4}{3x+12}.\dfrac{x+4}{2x-4}\)
z) \(\left(x^2-25\right):\dfrac{2x+10}{3x-7}\)
t) \(\left(\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}\right):\dfrac{4x}{10x-5}\)
w) \(\left(\dfrac{1}{x^2+x}-\dfrac{2-x}{x+1}\right):\left(\dfrac{1}{x}+x-2\right)\)
c: \(=x^2+6xy+9y^2\)
e: \(=x^4-4y^2\)
BT10: Thực hiện phép tính
\(a,\dfrac{4}{5}y^2x^5-x^3.x^2y^2\)
\(b,-xy^3-\dfrac{2}{7}y^2.xy\)
\(c,\dfrac{5}{6}xy^2z-\dfrac{1}{4}xyz.y\)
\(d,15x^4+7x^4-20x^2.x^2\)
\(e,\dfrac{1}{2}x^5y-\dfrac{3}{4}x^5y+xy.x^4\)
\(f,13x^2y^5-2x^2y^5+x^6\)
a: =-1/5x^5y^2
b: =-9/7xy^3
c: =7/12xy^2z
d: =2x^4
e: =3/4x^5y
f: =11x^2y^5+x^6