Question

Bài 4.Rút gọn các biểu thức sau

1) \(4x^2\left(5x^3-2x+3\right)\)

2) \(3y^2\left(4y^3+\frac{2}{3}y^2-\frac{1}{3}\right)\)

3) \(\left(5x^2-4x\right)\left(x-2\right)\)

4) \(\left(3x-5\right)\left(2x+11\right)-\left(2x+3\right)\left(3x+7\right)\)

Answer 1

a) \(4x^2\left(5x^3-2x+3\right)\)

\(=20x^5-8x^3+12x^2\)

b) \(3y^2\left(4y^3+\frac{2}{3}y^2-\frac{1}{3}\right)\)

\(=12y^5+2y^4-y^2\)

c) \(\left(5x^2-4x\right)\left(x-2\right)\)

\(=5x^3-14x^2+8x\)

d) \(\left(3x-5\right)\left(2x+11\right)-\left(2x+3\right)\left(3x+7\right)\)

\(=6x^2+22x-55-6x^2-23x-21\)

\(=-x-76\)

Answer 2

1, \(4x^2\left(5x^3-2x+3\right)=20x^5-8x^3+12x^2\)

2, \(3y^2\left(4y^3+\frac{2}{3}y^2-\frac{1}{3}\right)=12y^5+2y^4-y^2\)

3, \(\left(5x^2-4x\right)\left(x-2\right)=5x^3-10x^2-4x^2+8x=5x^3-14x^2+8x\)

4, \(\left(3x-5\right)\left(2x+11\right)-\left(2x+3\right)\left(3x+7\right)=6x^2+33x-10x-55-\left(6x^2+14x+9x+21\right)\)

\(=6x^2+23x-55-6x^2-23x-21=-76\)

Answer 3

1) 4x²( 5x³ - 2x + 3 ) = 20x⁵ - 8x³ + 12x²

2) 3y²( 4y³ + 2/3y² - 1/3 ) = 12y⁵ + 2y⁴ - y² 

3) ( 5x² - 4x )( x - 2 ) = 5x³ - 14x² + 8x

4) ( 3x - 5 )( 2x + 11 ) - ( 2x + 3 )( 3x + 7 )

= 6x² + 23x - 55 - ( 6x² + 23x + 21 )

= 6x² + 23x - 55 - 6x² - 23x - 21

= -76

Answer 4

1 , 4x^2 ( 5x^3-2x+3) 

= 20x^5 - 8x^3+12x^2

2 , 3y^2 ( 4y^3+2/3y^2-1/3) 

= 12y^5 + 2y^4-y^2

3 , (5x^2 - 4x) ( x-2)

= 5x^3 - 14x^2 + 8x

4, ( 3x - 5) ( 2x+11)-(2x+3) (3x+7)

= 6x^2 + 23x - 55 -( 6x^2 + 14x + 9x + 21)

= 6x^2 + 23x - 55 - 6x^2 + 14x + 9x + 21

= -76