1) Phân tích hằng đẳng thức:
a/ (12x - 5)2
b/ (4x2 - y)3
c/ (7x + 8)3
2) Phân tích đa thức thành nhân tử:
a/ x3 - 16x
b/ x2 - 12x + 36
c/ 1 - 8x3
d/ 1/25x2 - 1/64y2
e/ (x + 2xy)3 - (x - 2y)3
f/ -x3 + 9x2 - 27x + 27
3) Tìm x, biết:
a/ x2 - 8x + 16 = 0
b/ x2 - x + 1/4 = 0
c/ 5x(x - 1000) - x + 1000 = 0
*hạn: trước 11/10/2017
\(1,a,\left(12x-5\right)^2=12^2x^2-2.12.5x+5^2\)
\(b,\left(4x^2-y\right)^3=\left(4x^2\right)^3-3.\left(4x^2\right)^2y+3.4x^2.y^2-y^3=4x^6-3.16x^4y+12x^2y^2\)
\(c,\left(7x+8\right)^3=\left(7x\right)^3+3.\left(7x\right)^28+3.7x.8+8^3\)
\(a,x^3-16x=x\left(x^2-16\right)=x\left(x^2-4^2\right)=x\left(x-4\right)\left(x+4\right)\)
\(b,x^2-12x+36=x^2-2.x.6+6^2=\left(x-6\right)^2\)
\(1-8x^3=1^3-\left(2x\right)^3=\left(1-2x\right)\left(1^2+1.2x+\left(2x\right)^2\right)=\left(1-2x\right)\left(1+2x+4x^2\right)\)
\(d,\dfrac{1}{25}x^2-\dfrac{1}{64}y^2=\left(\dfrac{1}{5}x\right)^2-\left(\dfrac{1}{8}x\right)^2=\left(\dfrac{1}{5}x-\dfrac{1}{8}x\right)\left(\dfrac{1}{5}x+\dfrac{1}{8}x\right)=x\left(\dfrac{1}{5}-\dfrac{1}{8}\right)\left(\dfrac{1}{5}+\dfrac{1}{8}\right)\)
b3\(a,x^2-8x+16=x^2-2x4+4^2=\left(x-4\right)^2=0\Rightarrow x=4\)
\(b,x^2-x+\dfrac{1}{4}=x^2-2x\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2=\left(x-\dfrac{1}{2}\right)^2=0\Rightarrow x=\dfrac{1}{2}\)
\(c,5x\left(x-1000\right)-x+1000=5x\left(x-1000\right)-\left(x-1000\right)=\left(x-1000\right)\left(5x-1\right)=0\Rightarrow\left[{}\begin{matrix}x-1000=0\Leftrightarrow x=1000\\5x-1=0\Leftrightarrow x=\dfrac{1}{5}\end{matrix}\right.\)
