\(\left(x+1\right)^2+\left(2x-1\right)\left(2x+1\right)-5x\left(x-1\right)=7\)

\(x^2+2x+1+4x^2-1-5x^2+5x=7\)

\(\left(x^2+4x^2-5x^2\right)+\left(1-1\right)+\left(2x+5x\right)=7\)

\(7x=7\)

\(x=1\)

a) \(2x^2-2y^2\)

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

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

b) \(x^2-4x+4\)

\(=x^2-2\cdot x\cdot2+2^2\)

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

c) \(x^2+2x+1-y^2\)

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

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

d) \(x^2-4x\)

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

e) \(x^2+10x+25\)

\(=x^2+2\cdot x\cdot5+5^2\)

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

g) \(x^2-2xy+y^2-9\)

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

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

h) \(2x^2-2\)

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

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

i) \(5x^2-5xy+9x-9y\)

\(=5x\left(x-y\right)+9\left(x-y\right)\)

\(=\left(x-y\right)\left(5x+9\right)\)

k) \(y^2-4y+4-x^2\)

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

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

l) \(x^2-16\)

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

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

m) \(3x^2-3xy+2x-2y\)

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

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

o) \(3x^4-6x^3+3x^2\)

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

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

a) 2x² - 2y²

 = (2x - 2y)(2x + 2y)

 = 4(x - y)(x + y)

b) x² - 4x + 4

 = (x - 2)²

c) x² + 2x + 1 - y²

 = (x + 1)² - y²

 = (x + 1 - y)(x + 1 + y)

d) x² - 4x 

 = x(x - 4)

e) x² +10x + 25

 = (x + 5)²

g) x² - 2xy + y² - 9

= (x - y)² - 3²

 = (x - y - 3)(x - y + 3)

h) 2x² - 2

= 2(x² - 1) 

 = 2(x - 1)(x + 1)

i) 5x² - 5xy + 9x - 9y

  = 5x(x - y) + 9(x- y)

 = (5x + 9)(x - y)

k) y² - 4y + 4 - x²

 = (y - 2)² - x²

 = (y - 2 - x)(y - 2 + x)

l) x² - 16

 = x² - 4²

 = (x - 4)(x + 4)

m) 3x² - 3xy + 2x -2y

 = 3x(x - y) +2(x-y)

 = (3x + 2)(x - y)

o) 3x⁴ - 6x³ + 3x²

 = 3x⁴ - 3x³ - 3x³ + 3x²

 = 3x³(x - 1) - 3x²(x - 1)

 = (3x³ - 3x²)(x - 1)

 = 3x²(x - 1)(x - 1)

 = 3x².(x - 1)²

a b A B H K 1 2 1 2 2 1 1 2

Vì a // b => A₁ + H₁ = 180⁰ ( trong cùng phía )

Mà H₁ = 90⁰ => A₁ = 180⁰ - 90⁰ = 90⁰

Mặt khác ta có H₁ = K₁ = 90⁰ ( giả thiết )

=> A₁ = H₁ = K₁ = 90⁰

=> tứ giác ABHK là hình chữ nhật

vuông 

fyg ggy