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: \(\left(x-\frac{y}{3}\right)\left(x+\frac{y}{3}\right)=x^2-\frac{y^2}{9}\)
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: \(\left(2x+1\right)\left(2x-1\right)-\left(4x+1\right)\left(x+2\right)=8\)
=>\(4x^2-1-\left(4x^2+8x+x+2\right)=8\)
=>\(4x^2-1-4x^2-9x-2=8\)
=>-9x=8+2+1=11
=>\(x=-\frac{11}{9}\)
b: \(\left(x-5\right)^2-x\left(x+4\right)=9-2x\)
=>\(x^2-10x+25-x^2-4x=9-2x\)
=>-14x+25=9-2x
=>-12x=9-25=-16
=>x=16/12=4/3
c: \(\left(1-2x\right)^2-\left(2x-3\right)\left(2x+3\right)=9\)
=>\(4x^2-4x+1-\left(4x^2-9\right)=9\)
=>\(4x^2-4x+1-4x^2+9=9\)
=>-4x+10=9
=>-4x=-1
=>\(x=\frac14\)
d: \(\left(x+2\right)^2-\left(x+1\right)\left(x-3\right)=5x-7\)
=>\(x^2+4x+4-\left(x^2-3x+x-3\right)=5x-7\)
=>\(x^2+4x+4-\left(x^2-2x-3\right)=5x-7\)
=>\(x^2+4x+4-x^2+2x+3=5x-7\)
=>6x+7=5x-7
=>6x-5x=-7-7
=>x=-14
