\(\left(x+5\right)\left(x^2-5x+25\right)\)

\(=\left(x+5\right)\left(x^2-5.x+5^2\right)\)

\(=x^3+5^3\)

\(=x^3+125\)

3) \(27-y^3\)

\(=3^3-y^3\)

\(=\left(3-y\right)\left(9-3y+y^2\right)\)

\(\left(5x-y\right)^2\)

\(=25x^2-10xy+y^2\)

\(\left(5x-y\right)^2\)

\(=25x^2-10xy+y^2\)

Trả lời:

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

b, \(\left(12x^6y^5-3x^3y^4+4x^2y\right):6x^2y\)

\(=12x^6y^5:6x^2y^2-3x^3y^4:6x^2y+4x^2y+6x^2y\)

\(=2x^4y^3-\frac{1}{2}xy^3+\frac{2}{3}\)

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

b.\(\left(12x^6y^5-3x^3y^4+4x^2y\right):6x^2y=2x^4y^4-\frac{1}{2}xy^3+\frac{2}{3}\)

2)

\(y+y^2-y^3-y^4=0\)

\(\Leftrightarrow y\left(y+1\right)-y^3\left(y+1\right)=0\)

\(\Leftrightarrow\left(y-y^3\right)\left(y+1\right)=0\)

\(\Leftrightarrow y\left(1-y^2\right)\left(y+1\right)=0\)

\(\Leftrightarrow y\left(1-y\right)\left(y+1\right)^2=0\)

\(\Leftrightarrow y\in\left\{0;-1;1\right\}\)

3)

\(A=n^3+3n^2-n-3\)

\(=n^2\left(n+3\right)-\left(n+3\right)\)

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

\(=\left(n-1\right)\left(n+1\right)\left(n+3\right)\)

n lẻ nên \(\hept{\begin{cases}n-1\\n+1\\n+3\end{cases}}\)chẵn

\(\Rightarrow\left(n-1\right)\left(n+1\right)\left(n+3\right)⋮2^3=8\left(đpcm\right)\)

b) \(a^2+2ab+2cd+b^2-c^2-d^2\)

\(=\left(a^2+2ab+b^2\right)-\left(c^2-2cd+d^2\right)\)

\(=\left(a+b\right)^2-\left(c-d\right)^2\)

\(=\left(a+b+c-d\right)\left(a+b-c+d\right)\)

Ai giúp mk với mk đang cần gấp

Mk làm được hết

mà vẫn cứ sai hoài à

tìm mãi ko thấy lỗi sai

Bài 3  Tính nhanh

A, 892^2+892.216+108^2                 B, 36^2+26^2-52.36

  =892^2+2.892.108+108^2                 =36^2-52.62+26^2

  =(892+108)^2           

  =1000^2

  =1000000

Bài 4 Phân tích đa thức sau thành nhân tử   

X^3-2x^2+x

5(x-y)-y(x-y)

36-12x+x^2

4x^2+12x-9

Bài 3:

\(892^2+892.216+108^2=892^2+2.892.108+108^2=\left(892+108\right)^2=1000000\)

\(36^2+26^2-52.36=36^2-2.26.36+26^2=\left(36-26\right)^2=100\)

Bài 4: 

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

\(5.\left(x-y\right)-y.\left(x-y\right)=\left(5-y\right)\left(x-y\right)\)

\(36-12x+x^2=x^2-12x+36=x^2-2x.6+6^2=\left(x-6\right)^2\)

\(4x^2+12x-9=\left(2x\right)^2+2.2x.3+3^2=\left(2x+3\right)^2\)

1 ) \(a\left(m+n\right)+b\left(m+n\right)\)

   \(=\left(a+b\right)\left(m+n\right)\)

2 ) \(a^2\left(x+y\right)-b^2\left(x+y\right)\)

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

   \(=\left[\left(a-b\right).\left(a+3\right)\right]\left(x+y\right)\)

3 ) \(6a^2-3a+12ab\)

   \(=3a.2a-3a+3a.4b\)

   \(=3a.\left(2a-1+4b\right)\)

4 ) \(2x^2y^4-2x^4y^2+6x^3y^3\)

   \(=2x^2y^2.y^2-2x^2y^2.x^2+2x^2y^2.3xy\)

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

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

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

      \(=\left(x+y\right)^2.y\)

1)a(m+n)+b(m+n)

=(a+b)(m+n)

2)a²(x+y)-b²(x+y)

=(a²-b²)(x+y)

3)6a²-3a+12ab

=3a.2a-3a.(1-4b)

=3a.(2a-1+4b)

5)(x+y)³-x(x+y)²

=(x+y)(x+y)²-x(x+y)²

=(x+y)²(x+y-x)