a) (x² + 4)² - 16x²

= (x² + 4 + 16x²) (x² + 4 - 16x²)

b) x⁶ - y³

= (x²)³ - y³

= (x² - y) (x² + x².y + y²)

= (x² - y) (x² + x²y + y²)

còn lại tương tự nha!! 5768568768769687807905474576575684764756856876876846

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

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

b) \(\left(x+1\right)^3+\left(x-1\right)^3\)

\(=\left(x+1+x-1\right)\left[\left(x+1\right)^2-\left(x+1\right)\left(x-1\right)+\left(x-1\right)^2\right]\)

\(=2x\left[\left(x+1\right)^2-\left(x^2-1\right)+\left(x-1\right)^2\right]\)

c) \(9x^2-3x+2y-4y^2\)

\(=9x^2-4y^2-3x+2y\)

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

\(=\left(3x-2y\right)\left[3x+2y-1\right]\)

d) \(4x^2-4xy+2x-y+y^2\)

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

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

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

e) \(x^3+3x^2+3x+1-y^3\)

\(=\left(x+1\right)^3-y^3\)

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

g) \(x^3-2x^2y+xy^2-4x\)

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

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

\(=x\left[\left(x-y\right)^2-4\right]\)

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

a) (x + 2y)² - (x - y)²

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

= 3y(2x + y)

b) (x + 1)³ + (x - 1)³

= (x + 1 + x - 1)[(x + 1)² - (x + 1)(x - 1) + (x - 1)²]

= 2x(x² + 2x + 1 - x² + 1 + x² - 2x + 1)

= 2x(x² + 3)

c) 9x² - 3x + 2y - 4y²

= (9x² - 4y²) - (3x - 2y)

= (3x - 2y)(3x + 2y) - (3x - 2y)

= (3x - 2y)(3x + 2y - 1)

d) 4x² - 4xy + 2x - y + y²

= (4x² - 4xy + y²) + (2x - y)

= (2x - y)² + (2x - y)

= (2x - y)(2x - y + 1)

e) x³ + 3x² + 3x + 1 - y³

= (x³ + 3x² + 3x + 1) - y³

= (x + 1)³ - y³

= (x + 1 - y)[(x + 1)² + (x + 1)y + y²]

= (x - y + 1)(x² + 2x + 1 + xy + y + y²)

g) x³ - 2x²y + xy² - 4x

= x(x² - 2xy + y² - 4)

= x[(x² - 2xy + y²) - 4]

= x[(x - y)² - 2²]

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

a)  \(x^2\)\(+\)\(6x\)\(+\)\(9\)

\(=\left(x+3\right)^2\)

b)  \(x^3\)\(+\)\(3x^2\)\(+\)\(3x\)\(+\)\(1\)

\(=\left(x+1\right)^3\)

c)  \(8x^3\)\(-\)\(\frac{1}{8}\)

\(=\left(2x-\frac{1}{2}\right)\left(4x^2+x+\frac{1}{4}\right)\)

d)  \(10x\)\(-\)\(25\)\(-\)\(x^2\)

\(=\)\(-x^2\)\(+\)\(10\)\(-\)\(25\)

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

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

e)  \(\frac{1}{25}x^2\)\(-\)\(64y^2\)

=\(\left(\frac{1}{25}x-8y\right)\left(\frac{1}{5}x+8y\right)\)

\(a,\left(x-1\right)^2-2^2=\left(x-1-2\right)\left(x-1+2\right)=\left(x-3\right)\left(x+1\right)\\ b,=\left(2x\right)^2+2.2x.3+3^2\\ =\left(2x+3\right)^2\\ c,=x^3-\left(2y\right)^3\\ =\left(x-2y\right)\left(x^2+2xy+4y^2\right)\\ d,=x^3\left(x^2-1\right)-\left(x^2-1\right)\\ =\left(x^3-1\right)\left(x^2-1\right)\\ =\left(x-1\right)\left(x^2+x+1\right)\left(x-1\right)\left(x+1\right)\\ =\left(x-1\right)\left(x+1\right)\left(x^2+x+1\right)\)

\(e,=-4x^2\left(x-1\right)+\left(x-1\right)\\ =\left(1-4x^2\right)\left(x-1\right)\\ =\left(1-2x\right)\left(1+2x\right)\left(x-1\right)\)

\(f,=\left(2x\right)^3+3.\left(2x\right)^2.1+3.2x.1^2+1^3\\ =\left(2x+1\right)^3\)

\(a,=5\left(x-2y\right)\\ b,=3xy\left(x-2y\right)\\ c,=\left(x-y\right)\left(x+3\right)\\ d,=\left(x-1\right)\left(2x-4x^2\right)=2x\left(1-2x\right)\left(x-1\right)\\ e,=\left(x-2y\right)^2\\ f,=\left(3x-4y\right)\left(3x+4y\right)\\ g,=\left(x-3\right)\left(x^2+3x+9\right)\)

a. 5x - 10y 

= 5(x - 2y)

b. 3x²y - 6xy²

= 3xy(x - 2y)

c. x(x - y) - 3(y - x)

= x(x - y) + 3(x - y)

= (x + 3)(x - y)

d. 2x(x - 1) + 4x²(1 - x)

= 2x(x - 1) - 4x²(x - 1)

= (2x - 4x²)(x - 1)

= 2x(1 - 2x)(x - 1)

e. x² - 4xy + 4y²

= (x - 2y)²

f. 9x² - 16y²

= (3x - 4y)(3x + 4y)

g. x³ - 27

= (x - 3)(x² + 3x + 9)

a. 3xy( 4x + y - \(\dfrac{4}{3}\) )

b. 2x²( 3x + 1 )

c. (2x + 3 )( x - y )

d. xy( 1 - x )( x - 1 )

e. 6( 2x + 1 )( x + y )

a) (x + y)² - 2(x + y) + 1 

= (x + y)² - 2.1.(x + y) + 1

= (x + y - 1)²

b) x³ + 1 - x² - x

= (x³ - x²) - (x - 1) 

= x²(x - 1) - (x - 1)

= (x² - 1)(x - 1) = (x - 1)(x + 1)(x - 1) = (x - 1)²(x + 1) 

c) 27x³ - 0,001 

= \(\left(3x\right)^3-\frac{1}{1000}=\left(3x\right)^3-\left(\frac{1}{10}\right)^3=\left(3x-\frac{1}{10}\right)\left(9x^2+\frac{3}{10}x+\frac{1}{100}\right)\)

d) 125x³ - 1 =(5x)³ - 1 = (5x - 1)(25x² + 5x + 1) 

e) (x² + 4)² - 16x² 

= (x² + 4)² - (4x)²

= (x² - 4x + 4)(x² + 4x + 4) 

= (x - 2)²(x + 2)²

= [(x - 2)(x + 2)]²

a.\(\left(x+y\right)^2-2\left(x+y\right)+1\)

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

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

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

b.\(x^3+1-x^2-x\)

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

\(=x^2\left(x-1\right)-\left(x-1\right)\)

\(=\left(x-1\right)\left(x^2-1\right)\)

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

c.\(27x^3-0,001\)

\(=27x^3-\frac{1}{1000}\)

\(=\left(3x\right)^3-\left(\frac{1}{10}\right)^3\)

\(=\left(3x-\frac{1}{10}\right)\left(9x^2+0,3x+\frac{1}{100}\right)\)

d,\(125x^3-1\)

\(=\left(5x\right)^3-1^3\)

\(=\left(5x-1\right)\left(25x^2+5x+1\right)\)

e.\(\left(x^2+4\right)^2-16x^2\)

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

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

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

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

\(\left(x-3\right)\left(x-1\right)-3\left(x-3\right)\)

\(=\left(x-3\right)\left(x-1-3\right)\)

\(=\left(x-3\right)\left(x-4\right)\)

\(\left(x-1\right)\left(2x+1\right)+3\left(x-1\right)\left(x+2\right)\left(2x+1\right)\)

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

\(=\left(x-1\right)\left(2x+1\right)\left(3x+7\right)\)

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

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

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

\(=\left(x-5\right)\left(4x+1\right)\)

Còn lại bạn tự làm nhá

a: \(P=-3x^3+5x\)

\(=x\cdot\left(-3x^2\right)+x\cdot5\)

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

b: \(Q=\left(2x-1\right)+\left(x-2\right)\left(2x-1\right)\)

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

\(=\left(2x-1\right)\left(x-1\right)\)

c: \(R=4-16x^2\)

\(=4\cdot1-4\cdot4x^2\)

\(=4\left(1-4x^2\right)\)

\(=4\left(1-2x\right)\left(1+2x\right)\)

d: \(S=36-4x^2\)

\(=4\cdot9-4\cdot x^2\)

\(=4\left(9-x^2\right)\)

\(=4\left(3-x\right)\left(3+x\right)\)

e: \(T=8x^3-1\)

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

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

f: \(Q=8-x^3\)

\(=2^3-x^3\)

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

g: \(N=64-x^3\)

\(=4^3-x^3\)

\(=\left(4-x\right)\left(16+4x+x^2\right)\)