Rút gọn biểu thức

\(=\left(1-y^2\right)z+2y^2+\left(-x^2\right)y+2x^2-2\)

Ta có :

\(a\left(b^2+c^2+bc\right)+b\left(c^2+a^2+ac\right)+c\left(a^2+b^2+ab\right)\)

\(=ab^2+ac^2+abc+bc^2+a^2b+a^2c+b^2c+abc\)

\(=\left(ab^2+a^2b+abc\right)+\left(bc^2+b^2c+abc\right)+\left(ac^2+a^2c+abc\right)\)

\(=ab\left(a+b+c\right)+bc\left(a+b+c\right)+ac\left(a+b+c\right)\)

\(=\left(ab+bc+ac\right)\left(a+b+c\right)\)

Thanks rat nhieu

Phân tích 1000027 thành tích các thừa số được : 1000027 = 7x19x73x103

=> 1000027 là hợp số. 

a) (9+1)³  = 1000

Moi ng lam chi tiet nha!  Thanks trc

a) \(a^3+1+3a+3a^2=a^3+3a^2.1+3.a.1^2+1^3=\left(a+1\right)^3=\left(9+1\right)^3=10^3=1000\)

b)\(x^3+3x^2+3x=x^3+3x^2+3x+1-1=\left(x^3+3x^2.1+3.x.1^2+1^3\right)-1=\left(x+1\right)^3-1\)

\(=\left(19+1\right)^3-1=20^3-1=7999\)

x³ = x

x³ - x = 0

x . ( x² - 1 ) = 0

\(\Rightarrow\orbr{\begin{cases}x=0\\x^2-1=0\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x^2=1\end{cases}}\)

\(\Rightarrow\orbr{\begin{cases}x=0\\x=1\text{ hoặc }x=-1\end{cases}}\)

Vì 1 mũ bao nhiêu vẫn băng 1 

Nên 1^3=1

=>x=1

c/m răng 

( x^2-1 ) . P(x) = xP/x-2/ có ít nhất 3 nghiệm 

Tìm GTLN hay GTNN

A(x)=x^2+5

B(x)=(x+1)^2+(y+1)^2-3

\(\frac{2x+2}{\left(x+1\right)\left(x-1\right)}.ĐKXĐ:x\ne\pm1\)

\(=\frac{2\left(x+1\right)}{\left(x+1\right)\left(x-1\right)}=\frac{2}{x-1}\)

~~

e)(3x-1)(2x+7)-(x+1)(6x-5)=16

=>\(6x^2-2x+21x-7-6x^2-6x+5x+5\)=16

=>18x-2=16

=> 18x=18

=> x=1

b)\(x\left(x+1\right)\left(x+6\right)-x^3=5x\)

=>\(x\left(x+1\right)\left(x+6\right)-x^3-5x=0\)

=> \(x\left(x^2+x+6x+6\right)-x\left(x^2-5\right)=0\)

=>\(x\left[\left(x^2+7x+6\right)-\left(x^2-5\right)\right]=0\)

=> __x=1

     |__7x+1=0=> 7x=-1=> x=-1/7