Question

Đề bài: khai triển -> tổng quát

a, x²2 + 6x + 9

b, 25x² - 30x + 9

c, ( 2x - 3y ).( 2x + 3y )

d, ( x + 2y ).( x² - 2xy + 4y² )

e, 27x³ + 54x² + 36x + 8

f, ( 3x - 5y ).( 9x² + 15xy + 25y² )

g, x³ - 15x² + 75x - 125

Answer 1

Sửa lại:

a, x² + 6x + 9

Answer 2

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

Answer 3

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) \(x^3-15x^2+75x-125=x^3-3.x^2.5+3.x.5^2-5^3=\left(x-5\right)^3\)