Question

Điền các đơn thức thích hợp vào ô trống :

a) \(\left(3x+y\right)\left(.....-......+......\right)=27x^3+y^3\)

b) \(\left(2x-.....\right)\left(.....+10x+......\right)=8x^3-125\)

Answer 1

a) Ta có: 27\(x^3\)+ y\(^3\) = (3x)\(^3\) + y\(^3\)= (3x + y)[(3x)\(^2\) – 3x . y + y\(^2\)] = (3x + y)(9x\(^2\) – 3xy + y\(^2\))

Nên: (3x + y) (9x\(^2\) – 3xy + y\(^2\)) = 27x\(^3\) + y\(^3\)

b) Ta có: 8x\(^3\) – 125 = (2x)\(^3\) – 53= (2x – 5)[(2x)\(^2\) + 2x . 5 + 5\(^2\)]

= (2x – 5)(4x\(^2\) + 10x + 25)

Nên:(2x – 5)(4x\(^2\) + 10x + 25)= 8x\(^3\) – 125

Answer 2

Trả lời:

a) Ta có:

27x³ + y³ = (3x)³ + y³= (3x + y)[(3x)² – 3x . y + y²] = (3x + y)(9x² – 3xy + y²)

Nên: (3x + y) (9x² – 3xy + y² ) = 27x³ + y³

b) Ta có:8x³ - 125 = (2x)³ - 5³= (2x - 5)[(2x)² + 2x . 5 + 5²]

= (2x - 5)(4x² + 10x + 25)

Nên: (2x - 5)(4x²+ 10x +25 ) = 8x³ - 125

Answer 3

a) Ta có: 27x3 + y3 = (3x)3 + y3= (3x + y)[(3x)2 – 3x . y + y2] = (3x + y)(9x2 – 3xy + y2)

Nên: (3x + y) (9x2 – 3xy + y2) = 27x3 + y3

b) Ta có: 8x3 – 125 = (2x)3 – 53= (2x – 5)[(2x)2 + 2x . 5 + 52]

= (2x – 5)(4x2 + 10x + 25)

Nên:(2x – 5)(4x2 + 10x + 25)= 8x3 – 125

Answer 4

a, (3x+y)(9x²-3xy+y²)=27x³+y³

b, (2x-5)(4x²+10x+25)=8x³-125