a) Ta có: \(\dfrac{x^2+38x+4}{2x^2+17x+1}-\dfrac{3x^2-4x-2}{2x^2+17x+1}\)

\(=\dfrac{x^2+38x+4-3x^2+4x+2}{2x^2+17x+1}\)

\(=\dfrac{-2x^2+42x+6}{2x^2+17x+1}\)

c) Ta có: \(C=\dfrac{-x}{3x-2}+\dfrac{7x-4}{3x-2}\)

\(=\dfrac{-x+7x-4}{3x-2}\)

\(=\dfrac{6x-4}{3x-2}=2\)

a) (3x + 1)^2 - 2(3x + 1)(3x - 5) + (3x - 5)^2 

= 9x^2 + 6x + 1 - 18x^2 + 24x + 10 + 9x^2 - 30x + 25

= 36

b) (3x^2 - y)^2

= 9x^4 - 6x^2y + y^2

c) (3x + 5)^2 + (3x - 5)^2 - (3x + 2)(3x - 2)

= 9x^2 + 30x + 25 + 9x^2 - 30x + 25 - 9x^2 + 4

= 9x^2 + 54

d) 2x(2x - 1)^2 - 3x(x + 3)(x - 3) - 4x(x + 1)^2

= 8x^3 - 8x^2 + 2x - 3x^2 + 27x - 4x^3 - 8x^2 - 4x

= x^3 - 16x^2 + 25x

e) (x - 2)(x^2 + 2x + 4) - (x + 1)^2 + 3(x - 1)(x + 1)

= x^3 - 8 - x^2 - 2x - 1 + 3x^2 - 2

= x^3 + 2x^2 - 2x - 12

f) (x^4 - 5x^2 + 25)(x^2 + 5) - (2 + x^2)^2 + 3(1 + x^2)^2

= x^6 + 125 - 4 - 4x^2 - x^2 + 3 + 6x^2 + 3x^4

= x^6 + 2x^4 + 2x^2 + 124

\(a.\left(3x-2\right)^2+\left(3x+2\right)^2-2\left(\left(3x-2\right)\left(3x+2\right)\right)\\=9x^2-12x+4+9x^2+12x+4-18x^2+8\\ =18x^2+8-18x^2+8\\ =16\)

mấy câu còn lại tự động não nhé

a) (3x-2)² + (3x+2)² -2(3x-2)(3x+2)

=(3x-2)2

-2((3x-2)(3x+2)

+ (3x+2)²

=[(3x-2)-(3x+2)]²

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

=-4²

=8

b)(x-5)(x+5)-(x-6)(x-4)

=x²-5²-(x²-4x-6x+24)

=x²-25-x²+10x-24

=10x-49

c) đề sai , bạn xem lại chỗ 2(3x-1)(3x+2)

\(3x^3+6x^2-3x\Rightarrow ChonD\)

D

a: Sửa đề: 6x^3

\(\dfrac{6x^3-4x^2+3x-2}{3x-2}=\dfrac{2x^2\left(3x-2\right)+3x-2}{3x-2}=2x^2+1\)

b: \(\dfrac{6x^3-3x^2+4x+2}{3x^2+2}\)

\(=\dfrac{6x^3+4x-3x^2-2+4}{3x^2+2}\)

\(=2x-1+\dfrac{4}{3x^2+2}\)

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

=\(\left(3x^2-2y^2\right)\cdot2y^2\)

1) \(3x^2-9=3\left(x^2-3\right)\)

2) \(\dfrac{1}{2}x^2-2y^2\)

\(=\dfrac{1}{2}\left(x^2-4y^2\right)\)

\(=\dfrac{1}{2}\left(x-2y\right)\left(x +2y\right)\)

3) \(3x^2-12y^2\)

\(=3\left(x^2-4y^2\right)\)

\(=3\left(x-2y\right)\left(x+2y\right)\)

4) \(\dfrac{1}{3}x^2y^2-3x^2\)

\(=\dfrac{1}{3}x^2\left(y^2-9\right)\)

\(=\dfrac{1}{3}x^2\left(y-3\right)\left(y+3\right)\)

#Toru