a) x2 + 6x + 9 = (x + 3)2
b) 25x2 - 30x + 9 = (5x - 3)2
c) (2x - 3y)(2x + 3y) = (2x)2 - (3y)2 = 4x2 - 9y2
d) (x + 2y)(x2 + 2xy + 4y2) = (x + 2y)3
e) 27x3 + 54x2 + 36x + 8
Bài này chủ yếu là dùng HĐT
a) \(x^2+6x+9=\left(x+3\right)^2\)
b) \(25x^2-30x+9=\left(5x-3\right)^2\)
c) \(\left(2x-3y\right)\left(2x+3y\right)=4x^2-9y^2\)
d) \(\left(x+2y\right)\left(x^2-2xy+4y^2\right)=x^2-4y^2\)
e) \(27x^3+54x^2+36x+8=\left(3x\right)^3+3.\left(3x\right)^2.2+3.3x.2^2+2^3=\left(3x+2\right)^3\)
f) \(\left(3x-5y\right)\left(9x^2+15xy+25y^2\right)=\left(3x-5y\right)\left[\left(3x\right)^2+3x.5y+\left(5y\right)^2\right]=\left(3x\right)^3-\left(5y\right)^3=27x^3-125y^3\)
g) \(x^3-15x^2+75x-125=x^3-3.x^2.5+3.x.5^2-5^3=\left(x-5\right)^3\)