x³ + 8y³ - 3x² + 3x - 1

= ( x³ - 3x² + 3x - 1 ) + 8y³

= ( x - 1 )³ + ( 2y )³

= ( x + 2y - 1 )( x² - 2x + 1 - 2xy - 2y + 4y² ) 

Trả lời:

a, \(3^2\left(2x^2-5x-4\right)=18x^2-45x-36\)

b, \(\left(x+1\right)^2+\left(x-2\right)\left(x+3\right)-4x=x^2+2x+1+x^2+3x-2x-6-4x=2x^2-x-5\)

a, \(9\left(2x^2-5x-4\right)=18x^2-45x-36\)

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

\(=x^2+2x+1+x^2+x-6-4x=2x^2-x-5\)

Trả lời:

Câu 1: 

1, A = ( 2x - 3 )( 7x + 8 ) = 14x² + 16x - 21x - 24 = 14x² - 5x - 24

2, A = ( 3x + 7 )( x² - 3x + 2 ) = 3x³ - 9x² + 6x + 7x² - 21x + 14 = 3x³ - 2x² - 15x + 14 

3, A = ( x² - 2x + 5 )( x² + x - 1 ) = x⁴ + x³ - x² - 2x³ - 2x² + 2x + 5x² + 5x - 5 = x⁴ - x³ + 2x² + 7x - 5

4, A = ( x² - 3 )( x² - 7x + 6 ) = x⁴ - 7x³ + 6x² - 3x² + 21x - 18 = x⁴ - 7x³ + 3x² + 21x - 18 

5, A = ( 2x - y )( 2x + y ) = 4x² - y² 

6, A = ( x - 2y )( x² + 2xy + 4y² ) = x³ - 8y³ 

7, A = ( x + 3y )( x² - 3xy + 9y² ) = x³ + 27y³ 

8, A = ( xy + 1 )( xy - 1 ) = x²y² - 1 

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

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

\(B=\left(2a^2+1+2a\right)\left(2a^2+1-2a\right)-\left(2a^2+1\right)^2\)

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

\(C=\left[\left(x^2+3x+1\right)-\left(3x-1\right)\right]^2\)\(=\left(x^2+3x+1-3x+1\right)^2=\left(x^2+2\right)^2\)

1.\(\left(\frac{9}{x^3-9x}+\frac{1}{x+3}\right):\left(\frac{x-3}{x\left(x+3\right)}-\frac{x}{3x+9}\right)=\left(\frac{9+x\left(x-3\right)}{x\left(x-3\right)\left(x+3\right)}\right):\left(\frac{3x-9-x^2}{3x\left(x+3\right)}\right)=-\frac{1}{x-3}\)

2.\(\left(\frac{2\left(x+2\right)-2\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\right).\frac{\left(x+2\right)^2}{8}=\frac{4}{\left(x-2\right)\left(x+2\right)}.\frac{\left(x+2\right)^2}{8}=\frac{x-2}{2}\)

3.\(\left(\frac{3\left(3x+1\right)+2x\left(1-3x\right)}{\left(1-3x\right)\left(3x+1\right)}\right):\frac{2x\left(x+5\right)}{\left(1-3x\right)^2}=\frac{-6x^2+11x+3}{\left(1-3x\right)\left(3x+1\right)}.\frac{\left(1-3x\right)^2}{2x\left(x+5\right)}=\frac{-6x^2+11x+3}{\left(3x+1\right)}.\frac{\left(1-3x\right)}{2x\left(x+5\right)}\)

4.\(\left(\frac{x^2-\left(x-5\right)^2}{x\left(x-5\right)\left(x+5\right)}\right):\frac{2x-5}{x\left(x+5\right)}+\frac{x}{5-x}=\frac{10x-25}{x\left(x-5\right)\left(x+5\right)}.\frac{x\left(x+5\right)}{2x-5}+\frac{x}{5-x}=\frac{5}{x-5}-\frac{x}{x-5}=-1\)

\(1.A=14x^2+16x-21x-24=14x^2-5x-24\)

\(2.A=3x^3-2x^2-15x+14\)

\(3.A=x^4-x^3+2x^2+7x-5\)

\(4.A=x^4-7x^3+3x^2+21x-18\)

\(5.A=4x^2-y^2\)

\(6.A=x^3-8y^3\)

\(7.A=x^3+27y^3\)

\(8.A=x^2y^2-1\)