Question

[Đức Anh Lê]

Giúp mình với mình đang cần gấp quá. Cảm ơn các bạn nhiều

Answer 1

[Nguyễn Hoàng Minh]

2.

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

\(b,x^2-3y^2=\left(x-y\sqrt{3}\right)\left(x+y\sqrt{3}\right)\)

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

\(d,9\left(x-y\right)^2-4\left(x+y\right)^2\\ =\left[3\left(x-y\right)-2\left(x+y\right)\right]\left[3\left(x-y\right)+2\left(x+y\right)\right]\\ =\left(3x-3y-2x-2y\right)\left(3x-3y+2x+2y\right)\\ =\left(x-5y\right)\left(5x-y\right)\)

\(e,\left(4x^2-4x+1\right)-\left(x+1\right)^2\\ =\left(2x-1\right)^2-\left(x+1\right)^2\\ =\left(2x-1-x-1\right)\left(2x-1+x+1\right)\\ =3x\left(x-2\right)\)

\(f,x^3+27=\left(x+3\right)\left(x^2+3x+9\right)\)

\(g,27x^3-0,001=\left(3x-0,1\right)\left(9x^2+0,027x+0,01\right)\)

\(h,125x^3-1=\left(5x-1\right)\left(25x^2+5x+1\right)\)

Answer 2

[Lấp La Lấp Lánh]

Bài 3 : 

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

b) \(4x^2-12xy+9y^2=\left(2x-3y\right)^2\)

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

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

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

g) \(x^3+6x^2+12x+8=\left(x+2\right)^3\)

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

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