Question

Thu gọn biểu thức

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

2, \(\left(2x-1\right)^2-\left(x+2\right)^2-\left(2x-\dfrac{1}{2}\right)^2\)

3,\(\left(2x+1\right)^3-\left(2x-1\right)^3-24x^2\)

4, \(\left(x-2\right)^3-\left(2x+3\right)^3-7\cdot\left(1-x\right)^3\)

Answer 1

1)

(x-3).(x+3) - (x+1)²

= x² - 3² - x² - 2x - 1

= - 2x - 10

2)

(2x - 1)² - (x +2)² - (2x - \(\dfrac{1}{2}\))²

= 4x² - 4x +1 - x² - 4x - 4 - 4x² + 2x - \(\dfrac{1}{4}\)

= - x² - 6x - \(\dfrac{13}{4}\)

= - ( x² + 6x + \(\dfrac{13}{4}\) )

= - (x² + 2.3x + 9 - \(\dfrac{23}{4}\))

= - (x + 3)² + \(\dfrac{23}{4}\)

3)

(2x + 1)³ - (2x -1)³ - 24x²

= (2x -1 + 2)³ - (2x - 1)³ - 24x²

= (2x-1)³ + 3.(2x-1)².2 + 3.(2x-1).2² + 2³ - (2x - 1)³ - 24x²

= 6.(4x² - 4x + 1) + 24x - 12 +8 - 24x²

= 24x² - 24x + 6 +24x - 4 - 24x²

= 2

4)

(x-2)³ - (2x + 3)³ - 7.(1 - x)³

= x³ - 3.x².2 + 3x.2² - 2³ - 8x³ + 3.4x².3 - 3.2x.3² + 3³ - 7.(1³-3x + 3x² - x³)

= x³ - 3.x².2 + 3x.2² - 2³ - 8x³ + 3.4x².3 - 3.2x.3² + 3³ - 7 + 21x - 21x² + 7x³

= x³ - 6x² + 12x - 8 - 8x³ + 36x² - 54x² + 27 - 7 + 21x - 21x² + 7x³

= - 45x² + 33x + 12

= - 45(x² - \(\dfrac{33}{45}x-\dfrac{4}{15}\))

= \(-45.\left(x^2-2.\dfrac{11}{30}.x+\dfrac{121}{900}-\dfrac{361}{900}\right)\)

= \(-45.\left(x-\dfrac{11}{30}\right)^2+\dfrac{361}{20}\)