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

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

e: \(x^2-10x+25=\left(x-5\right)^2\)

g: \(x^2-64=\left(x-8\right)\left(x+8\right)\)

h: \(\left(x+y\right)^2-\left(x^2-y^2\right)\)

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

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

i: \(5x^2+5xy-x-y\)

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

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

k: \(x^2+2xy+y^2-25=\left(x+y-5\right)\left(x+y+5\right)\)

l: \(2xy-x^2-y^2+16\)

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

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

a: \(5x-15y=5\left(x-3y\right)\)

b: \(5x^2y^2+15x^2y+30xy^2=5xy\left(xy+3x+6y\right)\)

c: \(x^3-2x^2y+xy^2-9x\)

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

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

a) x³ + 2x²y +  xy² - 9x

= x(x² + 2xy + y² - 9)

= x(x+y)² - 9

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

b) 5x² - 10xy + 5y²

= 5(x² - 2xy + y²)

= 5(x-y)²

Có sai thì xin lỗi ạ

bạn tách ra từng ít câu 1 thôi ạ

a: \(=5x\left(xy^2+3x+6y^2\right)\)

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

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

d: \(=x\left(x^2-2xy+y^2-9\right)\)

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

e: \(=\left(x+y\right)^2-25=\left(x+y+5\right)\left(x+y-5\right)\)

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

a: \(3ab-6a^2b\)

\(=3ab\cdot1-3ab\cdot2a\)

=3ab(1-2a)

b: \(x^3-6x\)

\(=x\cdot x^2-x\cdot6\)

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

c: \(x^2-y^2-9x+9y\)

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

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

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

d: \(5x^2+10xy+5y^2\)

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

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

giải bài toán: cho tam giác MNP, NTlà phân giác của góc N biết MN=4cm, NT=10cm, MP=8cm:TínhTM, TP? 

\(a,5x^2y-10xy^2=5xy\left(x-2y\right)\\ b,x^2+2xy+y^2-5x-5y=\left(x+y\right)^2-5\left(x+y\right)=\left(x+y\right)\left(x+y-5\right)\\ c,x^2-6x+8=\left(x^2-2x\right)-\left(4x-8\right)=x\left(x-2\right)-4\left(x-2\right)=\left(x-2\right)\left(x-4\right)\\ d,5x^2-10xy+5y^2-20z^2=5\left(x^2-2xy+y^2-4z^2\right)=5\left[\left(x-y\right)^2-\left(2z\right)^2\right]=5\left(x-y-2z\right)\left(x-y+2z\right)\)

b: \(x^2-2xy+y^2-z^2\)

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

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

d: \(x^2+4x+3=\left(x+3\right)\left(x+1\right)\)

a) \(4x^2-16+\left(3x+12\right)\left(4-2x\right)\)

\(=\left(2x-4\right)\left(2x+4\right)-3\left(x+4\right)\left(2x-4\right)\)

\(=\left(2x-4\right)\left(2x+4-3x-12\right)\)

\(=-\left(2x-4\right)\left(x+8\right)\)

b) \(x^3+x^2y-15x-15y\)

\(=x^2\left(x+y\right)-15\left(x+y\right)\)

\(=\left(x+y\right)\left(x^2-15\right)\)

c) \(3\left(x+8\right)-x^2-8x\)

\(=3\left(x+8\right)-x\left(x+8\right)\)

\(=\left(x+8\right)\left(3-x\right)\)

d) \(x^3-3x^2+1-3x\)

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

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

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

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

d) \(5x^2-5y^2-20x+20y\)

\(=5\left(x^2-y^2\right)-20\left(x-y\right)\)

\(=5\left(x-y\right)\left(x+y\right)-20\left(x-y\right)\)

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

a: \(x^2-y^2-x-y\)

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

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

f: \(x^3-5x^2-5x+1\)

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

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