a: Ta có: \(\left(8x^3-4x^2\right):4x-\left(4x^2-5x\right):2x+\left(2x\right)^2\)

\(=2x^2-x-2x+\dfrac{5}{2}+4x^2\)

\(=6x^2-3x+\dfrac{5}{2}\)

b: Ta có: \(\left(3x^3-x^2y\right):x^2-\left(xy^2+x^2y\right):xy+2x\left(x-1\right)\)

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

\(=2x^2-2y\)

c: C=125x^3+150x^2+60x+8+125x^3-150x^2+60x-8-2(x^2-4)

=250x^3+120x-2x^2+8

=250x^3-2x^2+120x+8

d: D=(4x)^3-3^3-(4x)^3-3^3

=64x^3-27-64x^3-27

=-54

c) \(C=\left(5x+2\right)^3+\left(5x-2\right)^3-2\left(x-2\right)\left(x+2\right)\)

\(=\left[\left(5x\right)^3+3\cdot\left(5x\right)^2\cdot2+3\cdot5x\cdot2^2+2^3\right]+\left[\left(5x\right)^3-3\cdot\left(5x\right)^2\cdot2+3\cdot5x\cdot2^2-2^3\right]-2\left(x^2-4\right)\)

\(=125x^3+150x^2+60x+8+125x^3-150x^2+60x-8-2x^2+8\)

\(=\left(125x^3+125x^3\right)+\left(150x^2-150x^2-2x^2\right)+\left(60x+60x\right)+\left(8-8+8\right)\)

\(=250x^3-2x^2+120x+8\)

d) \(D=\left(4x-3\right)\left(16x^2+12x+9\right)-\left(4x+3\right)\left(16x^2-12x+9\right)\)

\(=\left(4x\right)^3-3^3-\left[\left(4x\right)^3+3^3\right]\)

\(=64x^3-27-\left(64x^3+27\right)\)

\(=64x^3-27-64x^3-27\)

\(=-27-27\)

\(=-54\)

A=-(3x+7)+(5x-2)+(2x-10)

=-3x-7+5x-2+2x-10

=(-3x+5x+2x)-(7+2+10)

=4x-19

B = (6x+8)-(4x-5)-3x

= 6x+8-4x+5-3x

= (6x-4x-3x) + (8+5)

= -x + 13

= 13-x

C = 2(5x+3) - (2x-1) + 12

= 10x+6 - 2x + 1 + 12

= (10x-2x) + (6+1+12)

= 8x + 19

D = (x+7)-3(x+1)+2x-5

= x+7-3x-3+2x-5

= (x-3x+2x) + (7-3-5)

= -1

\(=5x^2-4x^2+3x^2-6x=4x^2-6x\)

\(=4\cdot\left(-\dfrac{3}{2}\right)^2-6\cdot\dfrac{-3}{2}\)

\(=4\cdot\dfrac{9}{4}+6\cdot\dfrac{3}{2}\)

=9+9

=18

a) 5x² ( 3x² -7x+2)-15x(x-3)

=15x⁴-35x³+10x²-15x²+45x

=15x⁴-35x³-5x²+45x

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

=(x²-9)(x²+x-2x-2)

=(x²-9)(x²-x-2)

=x⁴-x³-2x²-9x²+9x+18

=x⁴-x³-11x²+9x+18

d)(2x+1)²+(4x-1)²+2(2x+1)(4x+1)

=2x²+4x+1-16x²-8x+1

=2x²+4x+1-16x²-8x+1+16x²-4x+8x-2

=2x²+7

e) (2x²-3x)(5x²-2x+1)-10x²(x+3)

=10x⁴ -4x³+2x²-15x³+6x²-3 -10x²-30x

=10x⁴-19x³-2x²-30x-3

thanks bn nka

a, (4x-3)(3x+2)-(6x+1)(2x-5)+1

=12x²-8x-9x+6-12x²+30x-2x+5+1

=11x+12

b, (3x+4)²+(4x-1)²+(2+5x)(2-5x)

=9x²+24x+16+16x²-8x+1+4-25x²

=16x+21

c, (2x+1)(4x²2x+1)+(2-3x)(4+6x+9x²)-9

=8x³+1+8-27x³-9

=-19x³

swingrock có thể giải thik rõ hơn đc ko ạ

Bạn ghi lại đề đi, khó nhìn quá

ĐKXĐ: \(x\ne1;x\ne-\dfrac{3}{2}\)

Ta có: \(\dfrac{3x^3-7x^2+5x-1}{2x^3-x^2-4x+3}=\dfrac{\left(x-1\right)^2\left(3x-1\right)}{\left(x-1\right)^2\left(2x+3\right)}=\dfrac{3x-1}{2x+3}\)