Question

Bài 1: Rút gọn các biểu thức:
a) (2x - 1)(2x + 1) - 5x(x - 1) + (5x - 4)(x - 3)
b) (3x + 2)(x² - 1) - 3x(x² - 2x - 1) + 2x(x - 3)(x - 1)

Bài 3: Rút gọn các biểu thức:
a) (4x - 1)(3x + 1) - 5x(x - 3) - (x - 4)(x - 3)

b) (5x - 2)(x + 1) - 3x(x² - x - 3) - 2x(x - 5)(x - 4)

(giúp mình gấp với ạ,mình cảm ơn)

Answer 1

Bài 1:

a) \(\left(2x-1\right)\left(2x+1\right)-5x\left(x-1\right)+\left(5x-4\right)\left(x-3\right)\)

\(=\left(4x^2-2x+2x-1\right)-\left(5x^2-5x\right)+\left(5x^2-15x-4x+12\right)\)

\(=\left(4x^2-1\right)-\left(5x^2-5x\right)+\left(5x^2-19x+12\right)\)

\(=4x^2-1-5x^2+5x+5x^2-19x+12\)

\(=\left(4x^2-5x^2+5x^2\right)+\left(5x-19x\right)+\left(-1+12\right)\)

\(=4x^2-14x+11\)

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

\(=\left(3x^3-3x+x^2-1\right)-\left(3x^3-6x^2-3x\right)+2x\left(x^2-x-3x+3\right)\)

\(=3x^3-3x+x^2-1-3x^3+6x^2+3x+\left(2x^3-8x^2+6x\right)\)

\(=7x^2-1+2x^3-8x^2+6x\) 

\(=2x^3-x^2+6x-1\)

Answer 2

bài 3:

a: \(\left(4x-1\right)\left(3x+1\right)-5x\left(x-3\right)-\left(x-4\right)\left(x-3\right)\)

\(=12x^2+4x-3x-1-5x^2+15x-\left(x^2-7x+12\right)\)

\(=7x^2+16x-1-x^2+7x-12\)

\(=6x^2+23x-13\)

b: \(\left(5x-2\right)\left(x+1\right)-3x\left(x^2-x-3\right)-2x\left(x-5\right)\left(x-4\right)\)

\(=5x^2+5x-2x-2-3x^3+3x^2+9x-2x\left(x^2-9x+20\right)\)

\(=-3x^3+8x^2+12x-2-2x^3+18x^2-40x\)

\(=-5x^3+26x^2-28x-2\)