1. Làm tính nhẩm:
a. 2x (x^2-7x-3)
b. ( - 2x^3 + 3/4y^2 - 7xy ) . 4xy^2
c. (25x^2 + 10xy + 4y^2). (5x-2y)
d. (5x^3 - x^2 + 2x - 3) . (4x^2-x+2)
2. Tính nhanh:
a. 2004^2 - 16
b. 892^2 + 892 . 216 + 108^2
c. 10,2 . 9,8 - 9,8 . 0,2 + 10,2^2 . 0,2
d. 36^2 + 26^2 - 52 . 36
3. Phân tích các đa thức sau thành nhân tử:
a. 4x-8y
b. x^2 + 2xy + y^2 - 16
c. 3x^2 + 5x - 3xy - 5y
4. Làm phép chia:
(6x^3 - 7x^2 - x + 2) : (2x+1)
5. Tìm x biết:
a. x(x-2) + x - 2 = 0
b. 5x(x-3) - x + 3 = 0
c. 3x(x-5) - ( x-1)(2+3x) = 30
d. (x+2)(x+3) - (x-2)(x+5) = 0
6. Tìm giá trị nhỏ nhất của biểu thức:
A = x^2 - 2x + 2
6.
\(A=x^2-2x+2\\ =x^2-2x+1+1\\ =\left(x-1\right)^2+1\\ \left(x-1\right)^2\ge0\forall x\\ \left(x-1\right)^2+1\ge1\forall x\)
Dấu "=" xảy ra khi \(\left(x-1\right)^2=0\Rightarrow x-1=0\Rightarrow x=1\)
Vậy \(Min_A=1\) khi \(x=1\)
5,
a,
\(x\left(x-2\right)+x-2=0\\ \left(x+1\right)\left(x-2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x+1=0\\x-2=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=-1\\x=2\end{matrix}\right.\)
b,
\(5x\left(x-3\right)-x+3=0\\ 5x\left(x-3\right)-\left(x-3\right)=0\\ \left(5x+1\right)\left(x-3\right)=0\\ \Rightarrow\left[{}\begin{matrix}5x+1=0\\x-3=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\dfrac{-1}{5}\\x=3\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=\dfrac{-1}{5}\\x=3\end{matrix}\right.\)
c,
\(3x\left(x-5\right)-\left(x-1\right)\left(2+3x\right)=30\\ 3x^2-15x-\left(2x-2+3x^2-3x\right)\\ 3x^2-15x-\left(3x^2-x-2\right)=30\\ 3x^2-15x-3x^2+x+2=30\\ -14x+2=30\\ -14x=28\\ x=-2\)
Vậy \(x=-2\)
d,
\(\left(x+2\right)\left(x+3\right)-\left(x-2\right)\left(x+5\right)=0\\ x^2+5x+6-\left(x^2+3x-10\right)=0\\ x^2+5x+6-x^2-3x+10\\ 8x+16=0\\ 8x=-16\\ x=-2\)
Vậy \(x=-2\)
3.
\(4x-8y=4\left(x-2y\right)\)
b,
\(x^2+2xy+y^2-16=\left(x+y\right)^2-4^2=\left(x+y+4\right)\left(x+y-4\right)\)
c,
\(3x^2+5x-3xy-5y\\ =3x^2-3xy+5x-5y\\ =3x\left(x-y\right)+5\left(x-y\right)\\ =\left(3x+5\right)\left(x-y\right)\)
Câu c e thấy nó sao sao í
a,
\(2004^2-16=2004^2-4^2=\left(2004+4\right)\left(2004-4\right)=2008\cdot2000=4016000\)
b,
\(892^2+892\cdot216+108^2=892^2+892\cdot2\cdot108+108^2=\left(892+108\right)^2=1000^2=1000000\)
d,
\(36^2+26^2-52\cdot36=36^2-2\cdot26\cdot36+26^2=\left(36-26\right)^2=10^2=100\)
P/S: e ms 12 tuổi thôi, đg xưng bn nhá