x² -10x + 25 - y²

= (x-5)² - y²

= (x-5+y).(x-5-y)

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

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

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

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Chúc mày học ngu

Chúc mày học ngu

Chúc mày học ngu

-x²+10x-25=-(x²-10x+25)=-(x²-2.5+25)=-(x-5)²

\(x^4+2x^3+10x-25\)

\(=x^4+5x^2+2x^3+10x-5x^2-25\)

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

a)Ta có:  \(x\left(x-y\right)+5x-5y=x\left(x-y\right)+\left(5x-5y\right)\)

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

b) \(x^2-y^2+10x+25=\left(x^2+10x+25\right)-y^2=\left(x+5\right)^2-y^2\)

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

d: \(=\left(x+1-5\right)\left(x+1+5\right)=\left(x-4\right)\left(x+6\right)\)

- x² + 10x - 25

= - ( x² - 10x + 25 )

= - ( x - 5 )²

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

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

b.\(x^4-x^3+x^2-1=x^3\left(x-1\right)+\left(x+1\right)\left(x-1\right)\)=\(\left(x-1\right)\left(x^3+x+1\right)\)

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

a,

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

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

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

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

a) \(y^2-x^2+10x-25=y^2-\left(x^2-10x+25\right)=y^2-\left(x^2-2.x.5+5^2\right)\)

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

b) \(\left(3x+1\right)^2=3x+1\Rightarrow\left(3x-1\right)^2-\left(3x+1\right)=0\)

\(\Rightarrow\left(3x+1\right)\left(3x+1-1\right)=0\Rightarrow\left(3x+1\right).3x=0\)

\(\Rightarrow\orbr{\begin{cases}3x+1=0\\3x=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{-1}{3}\\x=0\end{cases}}}\)

Ta có

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

\(\left(3x+1\right)^2-\left(3x+1\right)=0\)

\(\left(3x+1\right)\left(3x+1-1\right)=0\)

\(x\left(3x+1\right)=0\)\(\Rightarrow\orbr{\begin{cases}x=0\\3x+1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=0\\x=-\frac{1}{3}\end{cases}}}\)

10x-25-x^2

=-x^2+10x-25

= - (x^2-10x+25)

=-(x^2-2x5+25)

= -(x-5)^2