Câu 5 tim x

a)\(\left(x-1\right)^3-\left(x+3\right)\left(x^2-3x+9\right)+3\left(x^2-4\right)=2\)

\(\Leftrightarrow\left(x^3-3x^2+3x-1\right)-\left(x^3-3x^2+9x+3x^2-9x+27\right)+\left(3x^2-12\right)-2=0\)

\(\Leftrightarrow x^3-3x^2+3x-1-x^3+3x^2-9x-3x^2+9x-27+3x^2-12-2=0\)

\(\Leftrightarrow3x-42=0\)

\(\Leftrightarrow3x=-42\)

\(\Leftrightarrow x=-14\)

Vậy x=-14

b)\(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2+2\right)=0\)

\(\Leftrightarrow\left(x^3-2x^2+4x+2x^2-4x+8\right)-\left(x^3+2x\right)=0\)

\(\Leftrightarrow x^3-2x^2+4x+2x^2-4x+8-x^3-2x=0\)

\(\Leftrightarrow8-2x=0\)

\(\Leftrightarrow2x=8\)

\(\Leftrightarrow x=4\)

Vậy x=4

c)\(x\left(x-2\right)+x-2=0\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\end{matrix}\right.\)

Vậy x=2 ; x=-1

Câu 3: phân tích

a)\(4x-8y\)

\(=4\left(x-2y\right)\)

b)\(x^2+2xy+y^2-16\)

\(=\left(x+y\right)^2-4^2\)

\(=\left(x+y-4\right)\left(x+y+4\right)\)

c)\(3x^2+5x-3xy-5y\)

\(=3x^2-3xy+5x-5y\)

\(=3x\left(x-y\right)+5\left(x-y\right)\)

\(=\left(x-y\right)\left(3x+5\right)\)

=10
Tick nha
 

tính

1)\(\left(\dfrac{1}{2}\right)^2\)

\(=\dfrac{1}{2}\times\dfrac{1}{2}\)

\(=\dfrac{1}{4}\)

2)\(3,6^2\div1,2^2\)

\(=\left(\dfrac{18}{5}\right)^2\div\left(\dfrac{6}{5}\right)^2\)

\(=\left(\dfrac{18}{5}\times\dfrac{18}{5}\right)\div\left(\dfrac{6}{5}\times\dfrac{6}{5}\right)\)

\(=\dfrac{324}{25}\div\dfrac{36}{25}\)

\(=\dfrac{324}{25}\times\dfrac{25}{36}\)

\(=\dfrac{8100}{900}\)

\(=9\)

thương bằng \(-8x^3+12x^2-6x+6\)

phép chia hết

Bài 1: Thực hiện phép tính

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

\(=\left(2x^3-4x^2\right)+\left(3x^3-3x^2-6x\right)-\left(15-5x^2\right)\)

\(=2x^3-4x^2+3x^3-3x^2-6x-15+5x^2\)

\(=5x^3-2x^2-6x-15\)

k) \(\left(x-1\right)\left(x-3\right)-\left(4-x\right)\left(2x+1\right)-3x^2+2x-5\)

\(=\left(x^2-3x-x+3\right)-\left(8x+4-2x^2-x\right)-3x^2+2x-5\)

\(=x^2-3x-x+3-8x-4+2x^2+x-3x^2+2x-5\)

\(=-9x-6\)

Bài 1: thực hiện phép tính

g) \(\left(a+b\right)^3-\left(a-b\right)^3-2b^3\)

\(=\left(a^3+3a^2b+3ab^2+b^3\right)-\left(a^3-3a^2b+3ab^2-b^3\right)-2b^3\)

\(=a^3+3a^2b+3ab^2+b^3-a^3+3a^2b-3ab^2+b^3-2b^3\)

\(=6a^2b\)

h) \(\left(x-y\right)\left(x+y\right)\left(x^2+y^2\right)\left(x^4+y^4\right)\)

\(=\left(x^2-y^2\right)\left(x^6+x^2y^4+y^2x^4+y^6\right)\)

\(=x^8+x^4y^4+y^2x^6+x^2y^6-y^2x^6-x^2y^6-y^4x^4-y^8\)

\(=x^8-y^8\)

Bài 7: Cứng minh đẳng thức

b) \(\left(x^{n+3}-x^{n+1}.y^2\right)\div\left(x+y\right)=x^{n+2}-x^{n+1}.y\)

Biến đổi vế trái

\(\left(x^{n+3}-x^{n+1}.y^2\right)\div\left(x+y\right)\)

\(=\left(x^n.x^3-x^n.x.y^2\right)\div\left(x+y\right)\)

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

\(=x^{n+1}\left(x-y\right)\left(x+y\right)\div\left(x+y\right)\)

\(=x^{n+1}\left(x-y\right)\)

Biến đổi vế phải

\(x^{n+2}-x^{n+1}.y\)

\(=x^n.x^2-x^n.x.y\)

\(=x^n.x\left(x-y\right)\)

\(=x^{n+1}\left(x-y\right)\) bằng vế trái (điều phải chứng minh)

bài 7: Chứng minh đẳng thức

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

Biến đổi vế phải

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

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

\(=x^2+y^2\) bằng vế trái (điều phải chứng minh)

có,mik rất cần chi tiết bn làm giúp mik với nhé.Mik cảm ơn bn rất nhiều