Bài 4: Rút gọn các biểu thức sau
1) (x+1)³ − (x−4)(x+4) − x³
2) (x+2)³ −x(x+3)(x-3)−12x² -8
3) (x-2)^3-x(x-2)(x+2)+6x(x-3)
4) x(x-5)(x+5)-(x-5)³ +100x
5) (x-3y)³-(x-2y) (2y+x)
6) (-x-2y)³+x(2y-x)(x+2y)
7) -(2x-y)³-x(2x-y)² - y³
8) −x(x − y)²+(x − y)³ + y² (y−2x)

Question

Bài 4: Rút gọn các biểu thức sau
1) (x+1)³ − (x−4)(x+4) − x³
2) (x+2)³ −x(x+3)(x-3)−12x² -8
3) (x-2)^3-x(x-2)(x+2)+6x(x-3)
4) x(x-5)(x+5)-(x-5)³ +100x
5) (x-3y)³-(x-2y) (2y+x)
6) (-x-2y)³+x(2y-x)(x+2y)
7) -(2x-y)³-x(2x-y)² - y³ 
8) −x(x − y)²+(x − y)³ + y² (y−2x)

LuongLuong · Accepted Answer

$\displaystyle \begin{array}{{>{\displaystyle}l}}
1) \ ( x+1)^{3} \ −\ ( x−4)( x+4) −\ x^{3}\
=\ \left( x^{3} \ +\ 3x^{2} \ +\ 3x\ +\ 1 ight) \ -\ \left( x^{2} \ -\ 16 ight) \ -\ x^{3}\
=\ x^{3} \ +\ 3x^{2} \ +\ 3x\ +\ 1\ -\ x^{2} \ +\ 16\ -\ x^{3}\
=\ 2x^{2} \ +\ 3x\ +\ 17\
2) \ ( x+2)^{3} \ −x( x+3)( x-3) −12x^{2} \ -8\
=\ \left( x^{3} \ +\ 6x^{2} \ +\ 12x\ +\ 8 ight) \ -\ \left( x^{3} \ -\ 9x ight) \ -\ 12x^{2} \ -\ 8\
=\ x^{3} \ +\ 6x^{2} \ +\ 12x\ +\ 8\ -\ x^{3} \ +\ 9x\ -\ 12x^{2} \ -\ 8\
=\ 6x^{2} \ +\ 21x\
\
3) \ ( x-2)^{3} -x( x-2)( x+2) +6x( x-3)\
=\ \left( x^{3} \ -\ 6x^{2} \ +\ 12x\ -\ 8 ight) \ -\ \left( x^{3} \ -\ 4x ight) \ +\ 6x^{2} \ -\ 18x\
=\ x^{3} \ -\ 6x^{2} \ +\ 12x\ -\ 8\ -\ x^{3} \ +\ 4x\ +\ 6x^{2} \ -\ 18x\
=\ -2x\ -8\
4) \ x( x-5)( x+5) -( x-5)^{3} \ +100x\
=\ x^{3} \ -\ 25x\ -\ \left( x^{3} \ -\ 15x^{2} \ +\ 75x\ -\ 125 ight) +\ 100x\
=\ x^{3} \ -\ 25x\ -\ x^{3} \ +\ 15x^{2} \ -\ 75x\ +\ 125\ +\ 100x\
=\ 15x^{2} +125
\end{array}$

Timi · Answer

1) (x+1)³ − (x−4)(x+4) − x³
= (x+1)(x+1)(x+1) - (x-4)(x+4) - x³
= (x³ + 3x² + 3x + 1) - (x² - 16) - x³
= x³ + 3x² + 3x + 1 - x² + 16 - x³
= 2x² + 3x + 17

2) (x+2)³ −x(x+3)(x-3)−12x² -8
= (x+2)(x+2)(x+2) - x(x+3)(x-3) - 12x² - 8
= (x³ + 6x² + 12x + 8) - (x³ - 9x) - 12x² - 8
= x³ + 6x² + 12x + 8 - x³ + 9x - 12x² - 8
= -6x² + 21x

3) (x-2)^3-x(x-2)(x+2)+6x(x-3)
= (x-2)(x-2)(x-2) - x(x-2)(x+2) + 6x(x-3)
= (x³ - 6x² + 12x - 8) - (x³ - 4x) + 6x² - 18x
= x³ - 6x² + 12x - 8 - x³ + 4x + 6x² - 18x
= -10x + 4

4) x(x-5)(x+5)-(x-5)³ +100x
= x(x² - 25) - (x-5)(x-5)(x-5) + 100x
= x³ - 25x - (x³ - 15x² + 75x - 125) + 100x
= x³ - 25x - x³ + 15x² - 75x + 125 + 100x
= 15x²

5) (x-3y)³-(x-2y) (2y+x)
= (x-3y)(x-3y)(x-3y) - (x-2y)(2y+x)
= (x³ - 9xy + 27y²) - (x² - 4xy - 2xy - 2y²)
= x³ - 9xy + 27y² - x² + 6xy + 2y²
= x³ - x² - 3xy + 29y²

6) (-x-2y)³+x(2y-x)(x+2y)
= (-x-2y)(-x-2y)(-x-2y) + x(2y-x)(x+2y)
= (-x³ - 6x²y - 12xy² - 8y³) + (2xy² - x²y + 2x²y - x³)
= -x³ - 6x²y - 12xy² - 8y³ + 2xy² - x²y + 2x²y - x³
= -7x³ - 5x²y - 10xy² - 8y³

7) -(2x-y)³-x(2x-y)² - y³ 
= -(2x-y)(2x-y)(2x-y) - x(2x-y)(2x-y) - y³
= -(8x³ - 12x²y + 6xy² - y³) - x(4x² - 4xy + y²) - y³
= -8x³ + 12x²y - 6xy² + y³ - 4x³ + 4x²y - xy² - y³
= -12x³ + 16x²y - 7xy²

8) −x(x − y)²+(x − y)³ + y² (y−2x) 
= -x(x² - 2xy + y²) + (x - y)(x - y)(x - y) + y²(y - 2x)
= -x³ + 2x²y - xy² + x³ - 3x²y + 3xy² - y³ + y²y - 2xy²
= -y³ + y²y - 2xy²

Bài 4: Rút gọn các biểu thức sau 1) (x+1)³ − (x−4)(x+4) − x³ 2) (x+2)³ −x(x+3)(x-3)−12x² -8 3) (x-2)^3-x(x-2)(x+2)+6x(x-3) 4) x(x-5)(x+5)-(x-5)³ +100x 5) (x-3y)³-(x-2y) (2y+x) 6) (-x-2y)³+x(2y-x)(x+2y...