Đa thức này không phân tích được thành nhân tử.

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$-25x^6-y^8+10x^3{y}^4$

$=-(25x^6-10x^3{y}^4+y^8)$

$=-[{\left(5x^3\right)}^2-2.5x^3{y}^4+{\left(y^4\right)}^2]$

$=-{(5x^3-y^4)}^2$

rút gọn= 10x²y²-250x⁶y⁷=10x²y²(1-25x⁴y⁵)

thế nhá

1) -25x⁶ - y⁸ + 10x³y⁴ = -( 25x⁶ - 10x³y⁴ + y⁸ ) = -[ ( 5x³ )² - 2.5x³.y⁴ + ( y⁴ ) ] = -( 5x³ - y⁴ )²

2) 2x( 3x - 5 ) + 10 - 6x = 2x( 3x - 5 ) - 2( 3x - 5 ) = ( 3x - 5 )( 2x - 2 ) = 2( 3x - 5 )( x - 1 )

3) x² - 9 - x²( x² - 9 ) = ( x² - 9 ) - x²( x² - 9 ) = ( x² - 9 )( 1 - x² ) = ( x - 3 )( x + 3 )( 1 - x )( 1 + x )

4) 4x² - 9 - ( 3x + 1 )( 2x - 3 ) = ( 2x - 3 )( 2x + 3 ) - ( 3x + 1 )( 2x - 3 )

= ( 2x - 3 )[ ( 2x + 3 ) - ( 3x + 1 ) ]

= ( 2x - 3 )( 2x + 3 - 3x - 1 )

= ( 2x - 3 )( 2 - x )

5) 8x³ - y³ - 4x + 2y = ( 8x³ - y³ ) - ( 4x - 2y ) 

= [ ( 2x )³ - y³ ) - 2( 2x - y )

= ( 2x - y )( 4x² + 2xy + y² ) - 2( 2x - y )

= ( 2x - y )( 4x² + 2xy + y² - 2 )

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

\(12a^4-24a^2b^2-6ab=6a\left(2a^3-4ab^2-3b\right)\)

mk chỉnh đề

\(-25x^6-y^8+10x^3y^4=-\left(5x^3-y^4\right)^2\)

\(25-\left(3-x\right)^2=\left(5-3+x\right)\left(5+3-x\right)=\left(2+x\right)\left(8-x\right)\)

\(-25x^2\sqrt{2}+10x+4\sqrt{2}=-\sqrt{2}\left(25x^2-\dfrac{10}{\sqrt{2}}-4\right)=-\sqrt{2}.\left(\left(25x\right)^2-2.5.\dfrac{1}{\sqrt{2}}+\dfrac{1}{2}-\dfrac{5}{2}\right)=-\sqrt{2}\left[\left(5x-\dfrac{1}{\sqrt{2}}\right)^2-\dfrac{5}{2}\right]=-\sqrt{2}.\left(5x-\dfrac{1}{\sqrt{2}}-\dfrac{\sqrt{5}}{\sqrt{2}}\right).\left(5x-\dfrac{1}{\sqrt{2}}+\dfrac{\sqrt{5}}{\sqrt{2}}\right)=-\sqrt{2}.\left(5x-\dfrac{1+\sqrt{5}}{\sqrt{2}}\right)\left(5x-\dfrac{1-\sqrt{5}}{\sqrt{2}}\right)\)

??                       

Bạn trình bầy rõ ràng chút đi. Mk chẳng hiểu gì cả.

\(-25x^6-y^8+10x^3y^4\\ =-\left(25x^6-10x^3y^4+y^8\right)\\ =-\left[\left(5x^3\right)^2-2\cdot5x^3\cdot y^4+\left(y^4\right)^2\right]\\ \\ =\left(5x^3-y^4\right)^2\)

a) \(x^2-2x-15\)

\(\Leftrightarrow x^2-2x+1-16\)

\(\Leftrightarrow\left(x-1\right)^2-4^2\)

\(\Leftrightarrow\left(x-5\right)\left(x-3\right)\)

\(a,x^2-2x-15=\left(x^2-2x+1\right)-16.\)

\(=\left(x-1\right)^2-4^2\)

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

b)\(5x^2y^3-25x^3y^4+10x^3y^3\) 

 \(=5x^2y^3\left(1-5xy+2x\right)\) 

c)\(12x^2y-18xy^2-30y^2\) 

 \(=6y\left(2x^2-3xy-5y\right)\)