Bài 3
a) \(\left(x^2+x\right)^2+4x^2+4x\)
b) \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)+1\)
c) \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)
Những câu hỏi liên quan
giải pt :
a, \(\left(2x-6\right)\sqrt{x+4}-\left(x-5\right)\sqrt{2x+3}=3\left(x-1\right)\)
b, \(\left(4x+1\right)\sqrt{x+2}-\left(4x-1\right)\sqrt{x-2}=21\)
c, \(\left(4x+2\right)\sqrt{x+1}-\left(4x-2\right)\sqrt{x-1}=9\)
d, \(\left(2x-4\right)\sqrt{3x-2}+\sqrt{x+3}=5x-7+\sqrt{3x^2+7x-6}\)
giải pt :a,\(\left(2x+6\right)\sqrt{x+4}-\left(x-5\right)\sqrt{2x+3}=3\left(x-1\right)\)
b, \(\left(4x+1\right)\sqrt{x+2}-\left(4x-1\right)\sqrt{x-2}=21\)
c, \(\left(4x+2\right)\sqrt{x+1}-\left(4x-2\right)\sqrt{x-1}=9\)
d, \(\left(2x-4\right)\sqrt{3x-2}+\sqrt{x+3}=5x-7+\sqrt{3x^2+7x-6}\)
a) \(\left(x^2-16\right)\left(\dfrac{x}{4}-\dfrac{4x+5}{3}\right)=0\)
b) \(\left(4x-1\right)\left(x+5\right)=x^2-25\)
c) \(x\left(x+3\right)^3-\dfrac{x}{4}\left(x+3\right)=0\)
a) Ta có: \(\left(x^2-16\right)\left(\dfrac{x}{4}-\dfrac{4x+5}{3}\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x+4\right)\left(\dfrac{3x-16x-20}{12}\right)=0\)
\(\Leftrightarrow\left(x-4\right)\left(x+4\right)\cdot\left(-13x-20\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x+4=0\\-13x-20=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-4\\-13x=20\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-4\\x=\dfrac{-20}{13}\end{matrix}\right.\)
Vậy: \(x\in\left\{4;-4;\dfrac{-20}{13}\right\}\)
b) Ta có: \(\left(4x-1\right)\left(x+5\right)=x^2-25\)
\(\Leftrightarrow\left(4x-1\right)\left(x+5\right)-\left(x^2-25\right)=0\)
\(\Leftrightarrow\left(4x-1\right)\left(x+5\right)-\left(x+5\right)\left(x-5\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(4x-1-x+5\right)=0\)
\(\Leftrightarrow\left(x+5\right)\left(3x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+5=0\\3x+4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\3x=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-5\\x=-\dfrac{4}{3}\end{matrix}\right.\)
Vậy: \(x\in\left\{-5;\dfrac{-4}{3}\right\}\)
c) Ta có: \(x\left(x+3\right)^3-\dfrac{x}{4}\cdot\left(x+3\right)=0\)
\(\Leftrightarrow\left(x+3\right)\cdot\left[x\left(x+3\right)^2-\dfrac{1}{4}x\right]=0\)
\(\Leftrightarrow\left(x+3\right)\left[x\left(x^2+6x+9\right)-\dfrac{1}{4}x\right]=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^3+6x^2+9x-\dfrac{1}{4}x\right)=0\)
\(\Leftrightarrow\left(x+3\right)\cdot x\cdot\left(x^2+6x+\dfrac{35}{4}\right)=0\)
\(\Leftrightarrow x\left(x+3\right)\left(x^2+6x+9-\dfrac{1}{4}\right)=0\)
\(\Leftrightarrow x\left(x+3\right)\left[\left(x+3\right)^2-\dfrac{1}{4}\right]=0\)
\(\Leftrightarrow x\left(x+3\right)\left(x+3-\dfrac{1}{2}\right)\left(x+3+\dfrac{1}{2}\right)=0\)
\(\Leftrightarrow x\left(x+3\right)\left(x+\dfrac{5}{2}\right)\left(x+\dfrac{7}{2}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+3=0\\x+\dfrac{5}{2}=0\\x+\dfrac{7}{2}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\\x=-\dfrac{5}{2}\\x=-\dfrac{7}{2}\end{matrix}\right.\)
Vậy: \(x\in\left\{0;-3;-\dfrac{5}{2};-\dfrac{7}{2}\right\}\)
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Giải các phương trình sau:
a \(\left(x+2\right)\left(x+\text{4}\right)\left(x+6\right)\left(x+8\right)+16=0\)
b \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=0\)
c \(\left(4x+1\right)\left(12x-1\right)\left(3x+2\right)\left(x+1\right)-4=0\)
d \(\left(x^2-3x+2\right)\left(x^2+15x+56\right)+8=0\)
b: Ta có: \(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24=0\)
\(\Leftrightarrow\left(x^2+7x+10\right)\left(x^2+7x+12\right)-24=0\)
\(\Leftrightarrow\left(x^2+7x\right)^2+22\left(x^2+7x\right)+120-24=0\)
\(\Leftrightarrow x^2+7x+6=0\)
\(\Leftrightarrow\left(x+1\right)\left(x+6\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-6\end{matrix}\right.\)
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a) \(^{ }\left(7x+4\right)^2-\left(7x-4\right)\left(7x+4\right)\)
b) \(^{ }8\left(x-2\right)-3\left(x^2-4x-5\right)-5x^2\)
c) \(^{^{ }}\left(x+1\right)^3-\left(x-1\right)\left(x^2+x+1\right)-3x\left(x+1\right)\)
a: Ta có: \(\left(7x+4\right)^2-\left(7x-4\right)\left(7x+4\right)\)
\(=\left(7x+4\right)\left(7x+4-7x+4\right)\)
\(=8\left(7x+4\right)\)
=56x+32
b: Ta có: \(8\left(x-2\right)^2-3\left(x^2-4x-5\right)-5x^2\)
\(=8x^2-32x+32-3x^2+12x+15-5x^2\)
\(=-20x+47\)
c: Ta có: \(\left(x+1\right)^3-\left(x-1\right)\left(x^2+x+1\right)-3x\left(x+1\right)\)
\(=x^3+3x^2+3x+1-x^3+1-3x^2-3x\)
=2
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Phân tích các đa thức sau thành nhân tử ( đặt biến phụ )
a. left(x^2+xright)^2-14left(x^2+xright)+24
b. left(x^2+xright)^2+4x^2+4x-12
c. x^4+2x^3+5x^2+4x-12
d.left(x+1right)left(x+2right)left(x+3right)left(x+4right)+1
e. left(x+1right)left(x+3right)left(x+5right)left(x+7right)+15
f. left(x+1right)left(x+2right)left(x+3right)left(x+4right)-24
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Phân tích các đa thức sau thành nhân tử ( đặt biến phụ )
a. \(\left(x^2+x\right)^2-14\left(x^2+x\right)+24\)
b. \(\left(x^2+x\right)^2+4x^2+4x-12\)
c. \(x^4+2x^3+5x^2+4x-12\)
d.\(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1\)
e. \(\left(x+1\right)\left(x+3\right)\left(x+5\right)\left(x+7\right)+15\)
f. \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)-24\)
a) \(\left(x^2+x\right)^2-14\left(x^2+x\right)+24\)
Đặt \(x^2+x=y\) ta được:
\(y^2-14y+24\)
\(=x\left(y-12\right)-2\left(y-12\right)\)
\(=\left(y-2\right)\left(y-12\right)\)
Thay ngược trở lại:
\(\left(x^2+x-2\right)\left(x^2+x-12\right)\)
\(=\left(x-1\right)\left(x+2\right)\left(x-3\right)\left(x+4\right)\)
d) \(\left(x+1\right)\left(x+2\right)\left(x+3\right)\left(x+4\right)+1\)
\(=\left(x^2+5x+4\right)\left(x^2+5x+10\right)+1\)
Đặt \(x^2+5x+4=a\) được:
\(a\left(a+6\right)+1\)
\(=a^2+6a+1\)
\(=a^2+2.a.3+3^2-8\)
\(=\left(a+3\right)^2-\left(\sqrt{8}\right)^2\)
\(=\left(a+3-\sqrt{8}\right)\left(a+3+\sqrt{8}\right)\)
Mấy câu kia tương tự.
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Bài 2 . Thực hiện phép tính
a)\(6x^3\)\(\left(\dfrac{1}{3}x^2-\dfrac{5}{2}-\dfrac{1}{6}\right)\)\(-2x^5\)\(-x^3\)
b)\(\left(x-3\right)\left(x^2+3x-2\right)\)
c)\(\left(4x^3-4x^2-5x+4\right):\left(2x+1\right)\)
a: =2x^5-15x^3-x^2-2x^5-x^3=-16x^3-x^2
b: =x^3+3x^2-2x-3x^2-9x+6
=x^3-11x+6
c: \(=\dfrac{4x^3+2x^2-6x^2-3x-2x-1+5}{2x+1}\)
\(=2x^2-3x-1+\dfrac{5}{2x+1}\)
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a) \(6x^3\left(\dfrac{1}{3}x^2-\dfrac{5}{2}-\dfrac{1}{6}\right)-2x^5-x^3\)
\(=6x^3\left(\dfrac{1}{3}x^2-\dfrac{16}{6}\right)-2x^5-x^3\)
\(=2x^5-16x^3-2x^5-x^3\)
\(=-17x^3\)
b) \(\left(x+3\right)\left(x^2+3x-2\right)\)
\(=x^3+3x^2-2x+3x^2+9x-6\)
\(=x^3+6x^2+7x-6\)
c) \(\left(4x^3-4x^2-5x+4\right):\left(2x+1\right)\)
\(=2x^2+4x^3-2x-4x^2-\dfrac{5}{2}-5x+\dfrac{2}{x}+4\)
\(=4x^3-2x^2-7x+\dfrac{2}{x}+\dfrac{3}{2}\)
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Giải các PT sau
a,left(9^2-4right)left(x+1right)left(3x+2right)left(x^2-1right)
b,left(x-1right)^2-1+x^2left(1-xright)left(x+3right)
c,left(x^2-1right)left(x+2right)left(x-3right)left(x-1right)left(x^2-4right)left(x+5right)
d,x^4+x^3+x+10
e,x^3-7x+60
f,x^4-4x^3+12x-90
g,x^5-5x^3+4x0
h,x^4-4x^3+3x^2+4x-40
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Giải các PT sau
a,\(\left(9^2-4\right)\left(x+1\right)=\left(3x+2\right)\left(x^2-1\right)\)
b,\(\left(x-1\right)^2-1+x^2=\left(1-x\right)\left(x+3\right)\)
c,\(\left(x^2-1\right)\left(x+2\right)\left(x-3\right)=\left(x-1\right)\left(x^2-4\right)\left(x+5\right)\)
d,\(x^4+x^3+x+1=0\)
e,\(x^3-7x+6=0\)
f,\(x^4-4x^3+12x-9=0\)
g,\(x^5-5x^3+4x=0\)
h,\(x^4-4x^3+3x^2+4x-4=0\)
Bài 1 :Rút gọnleft(4x^2-3yright)a2y-left(3x^2-4yright)3y4x^2left(5x-3yright)-x^2left(4x+yright)2ax^2-aleft(1+2x^2right)-left{a-xleft(x+aright)right}Bài 2:Tìm xa)2xleft(x+1right)-x^2left(x+2right)+x^3-x+10b)4xleft(3x+2right)-6xleft(2x+5right)+21left(x-1right)0Bài 3:Rút gọnxleft(1+x+x^2+...+x^9right)-left(1+x+x^2+...+x^9right)
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Bài 1 :Rút gọn
\(\left(4x^2-3y\right)a2y-\left(3x^2-4y\right)3y\)
\(4x^2\left(5x-3y\right)-x^2\left(4x+y\right)\)
\(2ax^2-a\left(1+2x^2\right)-\left\{a-x\left(x+a\right)\right\}\)
Bài 2:Tìm x
a)\(2x\left(x+1\right)-x^2\left(x+2\right)+x^3-x+1=0\)
b)\(4x\left(3x+2\right)-6x\left(2x+5\right)+21\left(x-1\right)=0\)
Bài 3:Rút gọn
\(x\left(1+x+x^2+...+x^9\right)-\left(1+x+x^2+...+x^9\right)\)