1)P\(=9\left(x+3\right)^2-4\left(x-2\right)^2\)\(=\left(3x+9\right)^2-\left(2x-4\right)^2\)

      \(=\left(3x+9+2x-4\right)\left(3x+9-2x+4\right)\)(hằng đẳng thức số 3)

       \(=\left(5x+5\right)\left(x+13\right)\)

        \(=5\left(x+1\right)\left(x+13\right)\)

2)P\(=25\left(2x-y\right)^2-16\left(x+2y\right)^2\)\(=\left(10x-5y\right)^2-\left(4x+8y\right)^2\)

      \(=\left(14x+3y\right)\left(6x-13y\right)\)(tương tự câu 1)

x^3 - x + 3x^2y + 3xy^2 + y^3 - y

=x³+y³+3x²y+3xy²-x-y

=(x+y)(x²-xy+y²)+3xy(x+y)-(x+y)

=(x+y)(x²-xy+y²+3xy-1)

=(x+y)(x²+2xy+y²-1)

=(x+y)[(x+y)²-1]

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

x^2 + 5x - 6

=x²-x+6x-6

=x.(x-1)+6.(x-1)

=(x-1)(x+6)

Bạn học căn thức chưa ?

phan tich cac da thuc sau thanh nhan tu theo mau:

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

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

\(=x\left(\left(\sqrt{2}x\right)^2-1^2\right)\)\

\(=x\left(\sqrt{2}x-1\right)\left(\sqrt{2}x+1\right)\)

b)\(5x^2\left(x-1\right)-15x\left(x-1\right)\)

\(=\left(5x^2-15x\right)\left(x-1\right)\)

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

d)\(3x\left(x-2y\right)+6y\left(2y-x\right)\)

\(=3x\left(x-2y\right)-6y\left(x-2y\right)\)

\(=\left(3x-6y\right)\left(x-2y\right)\)

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

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

a, = (xy-y^2) + (2x-2y) = y(x-y) + 2.(x-y) = (x-y).(y+2) 

b, = (x+y)^2 - 9 = (x+y-3).(x+y+3)

\(xy-y^2-2x-2y\)   

=(xy-y).(2x-2y)

=y(x-y).2(x-y)

=(x-y).(y-2)

camr ơn bạn nha

Lưu ý rằng ba điều kiện đầu tiên yếu tố như (x + 1) ^ 2, do đó chúng ta có:
x^2 + 2x + 1 - y^2 = (x + 1)^2 - y^2. 

 (x + 1)^2 - y^2 = [(x + 1) + y][(x + 1) - y], từ a^2 - b^2 = (a + b)(a - b) 
= (x + y + 1)(x - y + 1).