a) \(=x^2-\left(2y\right)^2=\left(x-2y\right)\left(x+2y\right)\)

b) \(=x^2-\left(3y\right)^2=\left(x-3y\right)\left(x+3y\right)\)

c) \(=\left(2x-1\right)^2-\left(2y\right)^2=\left(2x-1-2y\right)\left(2x-1+2y\right)\)

d) \(=x^2-10xy+\left(5y\right)^2=\left(x-5y\right)^2\)

e) \(=\left(3x\right)^2-6x+1=\left(3x-1\right)^2\)

f) \(=\left(5x\right)^2+20x+4=\left(5x+2\right)^2\)

\(a)x^2-4y^2=(x-2y)(x+2y)\\b)x^2-9y^2=(x-3y)(x+3y)\\c)(2x-1)^2-4y^2=(2x-1-2y)(2x-1+2y)\\d) x^2-10xy+25y^2=(x-5y)^2\\e)9x^2-6x+1=(3x-1)^2\\f)25x^2+20x+4=(5x+2)^2\)

\(x^2+4y^2+9-4xy-6x+12y\)

\(=\left(x^2-4xy+4y^2\right)+\left(-6x+12y\right)+9\)

\(=\left(x-2y\right)^2-6\left(x-2y\right)+9\)

\(=\left(x-2y-3\right)^2\)

  3 - 6x + 3x^2  

 = 3 ( 1 - 2x + x^2 )

= 3( 1 - x )^2 

b, x^2 - 4xy + 4y^2 

= ( x)^2 + 2.x.2y + (2y)^2 

= ( x+ 2y)^2 

5xy³ + 30x²z² - 6x3yz - 25x²z

  => x(5y³ + 30xz² - 6x²yz - 25xz)

\(\left(x+2y-4\right)\left(x+2y+4\right)\)

a) \(4x^2-4xy+y^2-9\)

\(=\left(2x-y\right)^2-3^2\)

\(=\left(2x-y+3\right)\left(2x-y-3\right)\)

b) \(x^2-36+4xy+4y^2\)

\(=\left(4y^2+4xy+x^2\right)-36\)

\(=\left(2y+x\right)^2-6^2\)

\(=\left(2y+x+6\right)\left(2y+x-6\right)\)

c) \(9x^2-12xy-25+4y^2\)

\(=\left(9x^2-12xy+4y^2\right)-25\)

\(=\left(3x-2y\right)^2-5^2\)

\(=\left(3x-2y+5\right)\left(3x-2y-5\right)\)

d) \(25x^2+10x-4y^2+1\)

\(=\left(25x^2+10x+1\right)-4y^2\)

\(=\left(5x+1\right)^2-\left(2y\right)^2\)

\(=\left(5x+2y+1\right)\left(5x-2y+1\right)\)

(x+y)^2 - 5y^2

x^2- 4y^2 + 4xy

= x^2 + 4xy - 4y^2

=x^2 + 2x2y - (2y)^2

= ( x - 2y )^2

 x² - 4y² + 4xy = x² + 4xy - 4y² = - (x² - 4xy + 4y²) = - ((x² - 2x.2y + (2y)²)

= - ( x - 2y)²

ghytyyj

\(x^2-25-4xy+4y^2\)

\(=\left(x^2-4xy+4y^2\right)-25\)

\(=\left[x^2-2\cdot x\cdot2y+\left(2y\right)^2\right]-25\)

\(=\left(x-2y\right)^2-5^2\)

\(=\left(x-2y-5\right)\cdot\left(x-2y+5\right)\)