a) (3x+y)(9x²-3xy+y²) = 27x³+y³

b)(2x-5)(4x²+10x+25) = 8x³-125

a/9x² +3xy+y²

b/4x² +10x+5²

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

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

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

a) (3x +y)( 9x² - 3xy + y²)

b) (2x - 5)( 4x² + 10x + 25)

(đề bài này hay đó)

Thanks bn nhiều nhé

Rút gọn

( x+y+z)² - 2 ( x+y+z) (x+y)+(x+y)²

Giúp mình nhé các bạn, camon nhìu

\(a,\left(3x+y\right)\left(9x^2-3xy+y^2\right)=27x^3+y^3\)
\(b,\left(2x-5\right)\left(4x^2+10x+25\right)=8x^3-125\)

\(1, x^2-6x+9=(x+3)^2 \)

Tất cả các số 2 ở ngoài ngoặc là mũ 2 nhé các bạn. Mong các bạn đừng hiểu nhầm

a: =(6x)^2-(3x-2)^2

=(6x-3x+2)(6x+3x-2)

=(9x-2)(3x+2)

d: \(=\left[\left(x+1\right)^2-\left(x-1\right)^2\right]\left[\left(x+1\right)^2+\left(x-1\right)^2\right]\)

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

=8x(x^2+1)

e: =(4x)^2-2*4x*3y+(3y)^2

=(4x-3y)^2

f: \(=-\left(\dfrac{1}{4}x^4-2\cdot\dfrac{1}{2}x^2\cdot2y^3+4y^6\right)\)

\(=-\left(\dfrac{1}{2}x^2-2y^3\right)^2\)

g: =(4x)^3+1^3

=(4x+1)(16x^2-4x+1)

k: =x^3(27x^3-8)

=x^3(3x-2)(9x^2+6x+4)

l: =(x^3-y^3)(x^3+y^3)

=(x-y)(x+y)(x^2-xy+y^2)(x^2+xy+y^2)

Bài 1 : Khai triển .

a, \(\left(2x-y\right)^3=8x^3-12x^2y+6xy^2-y^3\)

b, \(27x^3+1=\left(3x+1\right)\left(9x^2-3x+1\right)\)

c, \(\left(2x\right)^3-125=\left(2x-5\right)\left(4x^2+10x+25\right)\)

Bài 2 :

a, \(x^2+10x+25=\left(x+5\right)^2=\left(x+5\right)\left(x+5\right)\)

b, \(16x^2-\left(x^2+4\right)^2=\left(4x-x^2+4\right)\left(4x+x^2+4\right)\)

c, \(x^2+3x^2+3x+1=4x^2+3x+1\)

\(=\left(2x\right)^2+\frac{2x.3}{2}+\frac{9}{4}-\frac{5}{4}=\left(2x+\frac{3}{2}\right)^2-\left(\sqrt{\frac{5}{4}}\right)^2\)

\(=\left(2x+\frac{3}{2}-\sqrt{\frac{5}{4}}\right)\left(2x+\frac{3}{2}+\sqrt{\frac{5}{4}}\right)\)