Bài 4:
a: \(x^2+6x+9=\left(x+3\right)^2\)
b: \(4x^2-4x+1=\left(2x-1\right)^2\)
c: \(9x^2-12xy+4y^2=\left(3x-2y\right)^2\)
d: \(\left(x-\dfrac{y}{3}\right)\left(x+\dfrac{y}{3}\right)=x^2-\dfrac{y^2}{9}\)
e: \(x^2-10x+25=\left(x-5\right)^2\)
f: \(4-4x^2+x^4=\left(2-x^2\right)^2\)
g: \(x^2-6xy+9y^2=\left(x-3y\right)^2\)
h: \(\left(2x+y^2\right)\left(2x-y^2\right)=4x^2-y^4\)
Bài 3:
a: Ta có: \(\left(2x+1\right)\left(2x-1\right)-\left(4x+1\right)\left(x+2\right)=8\)
\(\Leftrightarrow4x^2-1-4x^2-8x-x-2=8\)
\(\Leftrightarrow-9x=11\)
hay \(x=-\dfrac{11}{9}\)
b: Ta có: \(\left(x-5\right)^2-x\left(x+4\right)=9-2x\)
\(\Leftrightarrow x^2-10x+25-x^2-4x+2x=9\)
\(\Leftrightarrow-12x=-16\)
hay \(x=\dfrac{4}{3}\)
c: Ta có: \(\left(1-2x\right)^2-\left(2x-3\right)\left(2x+3\right)=9\)
\(\Leftrightarrow4x^2-4x+1-4x^2+9=9\)
\(\Leftrightarrow-4x=-1\)
hay \(x=\dfrac{1}{4}\)
d: Ta có: \(\left(x+2\right)^2-\left(x+1\right)\left(x-3\right)=-7+5x\)
\(\Leftrightarrow x^2+4x+4-x^2+3x-x+3-5x=-7\)
\(\Leftrightarrow x=-14\)
