Bài 1: Khai triển các đẳng thức sau:
a) (x+3)2
b) (4x2 - 9)2
c) (x + \(\dfrac{1}{2}\))2
d) (x - \(\dfrac{3}{2}\))2
e) x2 - 4
f) x2 - 289
Khai triển các hằng đẳng thức sau:
a) (2x-3)2 b) (2x+\(\dfrac{1}{2}\))2 c) (2x-\(\dfrac{1}{3}\))3
d) (x2+2y)3 e) 27-\(\dfrac{x^3}{8}\) f) 1253-64x3
GIẢI CHI TIẾT GIÚP MÌNH NHA.CẢM ƠN.
a) \(=4x^2-12x+9\)
b) \(=4x^2+2x+\dfrac{1}{4}\)
c) \(=4x^2-\dfrac{4}{3}x+\dfrac{1}{9}\)
d) \(=\left(x^2+2y\right)\left(x^4-2x^2y+4y^2\right)\)
e) \(=\left(3-\dfrac{x}{2}\right)\left(9+\dfrac{3x}{2}+\dfrac{x^2}{4}\right)\)
f) \(=\left(125-4x\right)\left(125^2+500x+16x^2\right)\)
Khai triển các hằng đẳng thức sau.
a) (x+1)3 b) (2x+3)3 c) (x+\(\dfrac{1}{2}\))3 d) (x2-2)3
e) (2x-3y)3
Giúp mình nha
\(a,=x^3+3x^2+3x+1\\ b,=8x^3+36x^2+54x+27\\ c,=x^3+\dfrac{3}{2}x^2+\dfrac{3}{4}x+\dfrac{1}{8}\\ d,=x^6-6x^4+12x^2-8\\ e,=8x^3-36x^2y+54xy^2-27y^3\)
chúng minh giá trị biểu thức sau ko phụ thuộc vào giá trị biến
a) (x-1)(x-2)(1+x+x2)(4+2x+x2)-x6+9x3
b) (\(\dfrac{1}{3}\)+2x)(4x2-\(\dfrac{2}{3}\)x+\(\dfrac{1}{9}\))-(2x-\(\dfrac{1}{3}\))(4x2+\(\dfrac{2}{3}\)x+\(\dfrac{1}{4}\))
c) (x-1)3-(x-1)(x2+x+1)-3(1-x)x
d) (x2-y2)(x2+xy+y2)(x2-xy+y2)+y6-x6
Mọi người giúp em vs ạ
a) Ta có: \(\left(x-1\right)\left(x-2\right)\left(x^2+x+1\right)\left(x^2+2x+4\right)-x^6+9x^3\)
\(=\left(x-1\right)\left(x^2+x+1\right)\left(x-2\right)\left(x^2+2x+4\right)-x^6+9x^3\)
\(=\left(x^3-1\right)\left(x^3-8\right)-x^6+9x^3\)
\(=x^6-9x^3+8-x^6+9x^3=8\)
b) Ta có: \(\left(\dfrac{1}{3}+2x\right)\left(\dfrac{1}{9}-\dfrac{2}{3}x+4x^2\right)-\left(2x-\dfrac{1}{3}\right)\left(4x^2+\dfrac{2}{3}x+\dfrac{1}{4}\right)\)
\(=\dfrac{1}{27}+8x^3-8x^3+\dfrac{1}{27}\)
\(=\dfrac{2}{27}\)
c) Ta có: \(\left(x-1\right)^3-\left(x-1\right)\left(x^2+x+1\right)-3x\left(1-x\right)\)
\(=x^3-3x^2+3x-1-x^3+1-3x+3x^2\)
=0
d) Ta có: \(\left(x^2-y^2\right)\left(x^2+xy+y^2\right)\left(x^2-xy+y^2\right)-x^6+y^6\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)\left(x+y\right)\left(x^2-xy+y^2\right)-x^6+y^6\)
\(=\left(x^3-y^3\right)\left(x^3+y^3\right)-x^6+y^6\)
\(=x^6-y^6-x^6+y^6=0\)
Bài 5: Tìm nghiệm của các đa thức sau: Dạng 1: a) 4x + 9 b) -5x + 6 c) 7 – 2x d) 2x + 5 Dạng 2: a) ( x+ 5 ) ( x – 3) b) ( 2x – 6) ( x – 3) c) ( x – 2) ( 4x + 10 ) Dạng 3: a) x2 -2x b) x2 – 3x c) 3x2 – 4x d) ( 2x- 1)2 Dạng 4: a) x2 – 1 b) x2 – 9 c)– x 2 + 25 d) x2 - 2 e) 4x2 + 5 f) –x 2 – 16 g) - 4x4 – 25 Dạng 5: a) 2x2 – 5x + 3 b) 4x2 + 6x – 1 c) 2x2 + x – 1 d) 3x2 + 2x – 1
3. Tìm nghiệm của các đa thức sau:
a) x + 7; b) \(\dfrac{1}{2}\)x - 4; c) - 8x + 20; d) x2 -100;
e) 4x2 -81; f) x2 - 7; g) x2 - 9x; h) x3 + 3x.
b: 1/2x-4=0
=>1/2x=4
hay x=8
a: x+7=0
=>x=-7
e: 4x2-81=0
=>(2x-9)(2x+9)=0
=>x=9/2 hoặc x=-9/2
g: x2-9x=0
=>x(x-9)=0
=>x=0 hoặc x=9
a)\(x+7=0=>x=-7\)
b)\(\dfrac{1}{2}x-4=0=>\dfrac{1}{2}x=4=>x=8\)
c)\(-8x+20=0=>-8x=-20=>x=\dfrac{5}{2}\)
d)\(x^2-100=0=>x^2=100=>\left[{}\begin{matrix}x=10\\x=-10\end{matrix}\right.\)
e)\(4x^2-81=0=>4x^2=81=>x^2=\dfrac{81}{4}=>\left[{}\begin{matrix}x=\dfrac{9}{2}\\x=-\dfrac{9}{2}\end{matrix}\right.\)
f)\(x^2-7=0=>x^2=7=>x=\sqrt{7}\)
g)\(x^2-9x=0=>x\left(x-9\right)=0=>\left[{}\begin{matrix}x=0\\x=9\end{matrix}\right.\)
3. Tìm nghiệm của các đa thức sau:
a) x + 7; b) \(\dfrac{1}{2}\)x - 4; c) - 8x + 20; d) x2 -100;
e) 4x2 -81; f) x2 - 7; g) x2 - 9x; h) x3 + 3x.
a: x+7=0
nên x=-7
b: x-4=0
nên x=4
c: -8x+20=0
=>-8x=-20
hay x=5/2
d: x2-100=0
=>(x-10)(x+10)=0
=>x=10 hoặc x=-10
a) x +7 =0
=>x = -7
b) x - 4 =0=>x = 4
c) -8x + 20 = 0 =>-8x =-20 =>\(x=-\dfrac{20}{-8}=\dfrac{5}{2}\)
d)\(x^2-100=0=>x^2=100>\left[{}\begin{matrix}x=10\\x=-10\end{matrix}\right.\)
e)\(4x^2-81=0=>4x^2=81=>x^2=\dfrac{81}{4}=>\left[{}\begin{matrix}x=\dfrac{9}{2}\\x=-\dfrac{9}{2}\end{matrix}\right.\)
f)\(x^2-7=0=>x^2=7=>x=\sqrt{7}\)
g)\(x^2-9x=0=>x\left(x-9\right)=0=>\left[{}\begin{matrix}x=0\\x=9\end{matrix}\right.\)
H)\(x^3+3x=0=>x\left(x^2 +3\right)=0=>\left[{}\begin{matrix}x=0\\x^2=-3\left(vl\right)\end{matrix}\right.\)
Bài 1: Phân tích các đa thức sau thành nhân tử
a. 1 - 4x2
b. 8 - 27x3
c. 27 + 27x + 9x 2 + x3
d. 2x3 + 4x2 + 2x
e. x2 - 5x - y2 + 5y
f. x2 - 6x + 9 - y2
g. 10x (x - y) - 6y(y - x)
h. x2 - 4x - 5
i. x4 - y4
Bài 2: Tìm x, biết
a. 5(x - 2) = x - 2
b. 3(x - 5) = 5 - x
c. (x +2)2 - (x+ 2) (x - 2) = 0
Bài 3: Tìm giá trị nhỏ nhất của biểu thức
a. A = x2 - 6x + 11
b. B = 4x2 - 20x + 101
c. C = -x2 - 4xy + 5y2 + 10x - 22y + 28
a.
\(1-4x^2=\left(1-2x\right)\left(1+2x\right)\)
b.
\(8-27x^3=\left(2\right)^3-\left(3x\right)^3=\left(2-3x\right)\left(4+6x+9x^2\right)\)
c.
\(27+27x+9x^2+x^3=x^3+3.x^2.3+3.3^2.x+3^3\)
\(=\left(x+3\right)^3\)
d.
\(2x^3+4x^2+2x=2x\left(x^2+2x+1\right)=2x\left(x+1\right)^2\)
e.
\(x^2-y^2-5x+5y=\left(x-y\right)\left(x+y\right)-5\left(x-y\right)\)
\(=\left(x-y\right)\left(x+y-5\right)\)
f.
\(x^2-6x+9-y^2=\left(x-3\right)^2-y^2=\left(x-3-y\right)\left(x-3+y\right)\)
g. 10x(x-y)-6y(y-x)
=10x(x-y)+6y(x-y)
=(x-y)(10x+6y)
h.x2-4x-5
=(x-5)(x+1)
i.x4-y4 = (x2-y2)(x2+y2)
B2.
a.5(x-2)=x-2
⇔5(x-2)-(x-2)=0
⇔4(x-2)=0
⇔x=2
b.3(x-5)=5-x
⇔3(x-5)+(x-5)=0
⇔4(x-5)=0
⇔x=5
c.(x+2)2-(x+2)(x-2)=0
⇔(x+2)[(x+2)-(x-2)]=0
⇔4(x+2)=0
⇔x=-2
Khai triển các hằng đẳng thức sau:
a) (3x-2)2 b) (\(\dfrac{x}{3}\)+y3)2 c) 9x2 -225
d) (2x-3y)3 e) (2x2+\(\dfrac{3}{2}\))3 f) (-2xy2+\(\dfrac{1}{2}\)x3y)3
Giải chi tiết giúp mình nha.Cảm ơn
a) \(\left(3x-2\right)^2=\left(3x\right)^2-2.3x.2+2^2=9x^2-12x+4\)
b) \(\left(\dfrac{x}{3}+y^3\right)^2=\left(\dfrac{x}{3}\right)^2+2\dfrac{x}{3}y^3+\left(y^3\right)^2=\dfrac{x^2}{9}+\dfrac{2}{3}xy^3+y^6\)
c) \(9x^2-225=\left(3x\right)^2-\left(15\right)^2=\left(3x-15\right)\left(3x+15\right)\)
d) \(\left(2x-3y\right)^3=\left(2x\right)^3-3\left(2x\right)^23y+3.2x\left(3y\right)^2-\left(3y\right)^3=8x^3-3.4x^2.3y+6x.9y^2-27y^3=8x^3-36x^2y+54xy^2-27y^3\)
e) \(\left(2x^2+\dfrac{3}{2}\right)^3=\left(2x^2\right)^3+3\left(2x^2\right)^2\dfrac{3}{2}+3.2x^2\left(\dfrac{3}{2}\right)^2+\left(\dfrac{3}{2}\right)^3=8x^6+3.4x^4.\dfrac{3}{2}+6x^2.\dfrac{9}{4}+\dfrac{27}{8}=8x^6+18x^4+\dfrac{27}{2}x^2+\dfrac{27}{8}\)
f) \(\left(-2xy^2+\dfrac{1}{2}x^3y\right)^3=\left(-2xy^2\right)+3\left(-2xy^2\right)^2\dfrac{1}{2}x^3y+3\left(-2xy^2\right)\left(\dfrac{1}{2}x^3y\right)^2+\left(\dfrac{1}{2}x^3y\right)^3=-8x^3y^6+3.4x^2y^4.\dfrac{1}{2}x^3y-6xy^2.\dfrac{1}{4}x^6y^2+\dfrac{1}{8}x^9y^3=-8x^3y^6+6x^5y^5-\dfrac{3}{2}x^7y^4+\dfrac{1}{8}x^9y^3\)
Bài 1 , Khai triển các hằng đẳng thức sau :
a , ( x + 2 )2 b, ( x - 1 )2 c, ( x2+ y2 )2
\(a,\left(x+2\right)^2=x^2+4x+4\\ b,\left(x-1\right)^2=x^2-2x+1\\ c,\left(x^2+y^2\right)^2=x^4+2x^2y^2+y^4\)
a) = x2 + 4x + 4
b) = x2 - 2x + 1
c) x4 + 2x2y2 + y4