-25x⁶ - y⁸ + 10x³y⁴

Đặt x³ = a ; y⁴ = b

Đa thức đã cho trở thành

-25a² - b² + 10ab

= -( 25a² - 10ab + b² )

= -( 5a - b )²

= -( 5x³ - y⁴ )²

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 )

Mình sửa: Bài 1
2)x²+3x-15

a) x² + 6x + 9 = x² + 2 . x . 3 + 3² = (x + 3)²

b) 10x – 25 – x² = -(-10x + 25 +x²) = -(25 – 10x + x²)

                         = -(5² – 2 . 5 . x – x²) = -(5 – x)²

c) 8x³ - 1/8 = (2x)³ – (1/2)³ = (2x - 1/2)[(2x)² + 2x . 12 + (1/2)²]

                    ^{= (2x - 1/2)(4x2 + x + 1/4)} 

d)1/25x² – 64y² = (1/5x)2(1/5x)2- (8y)² = (1/5x + 8y)(1/5x - 8y)

\(x^2-7x+10\)

\(=x^2-2x-5x+10\)

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

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

học tốt

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

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

thế nhá

a) 10x + 15y = 5(2x + 3y)

b) x² - 2xy - 4 + y²

= (x² - 2xy + y²)  - 4

= (x - y)² - 2²

= (x - y + 2)(x - y - 2)

c) x(x + y) - 3x - 3y

= x(x + y) -3(x + y)

= (x - 3)(x + y)

a, \(10x+15y=5\left(2x+3y\right)\)

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

c, \(x\left(x+y\right)-3x-3y=x\left(x+y\right)-3\left(x+y\right)=\left(x-3\right)\left(x+y\right)\)

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

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

mk chỉnh đề

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

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

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

e: \(=\left(x-2\right)\left(x-3\right)\)

a) x(4y-10x)

b)3(x+2y)+(x+1)

c)(5x-y)(5x+y)

d)5x(y-z)²

e)(x-3)(x-2)

f)(2x+y)³