Question

rút gọn các biểu thức sau:

a, (2x + 3)^2 + (2x - 3)^2 - 2(4x^2 - 9)

b, (x + 2)^3 + (x-2)^3 + x^3 - 3x(x + 2)(x - 2)

áp dụng hằng đẳng thức nhé

Giúp mình nha các tình yêu tối nay mình phải đi hok rồi!!

Answer 1

a) ta có : \(\left(2x+3\right)^2+\left(2x-3\right)^2-2\left(4x^2-9\right)\)

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

\(=\left(\left(2x+3\right)+\left(2x-3\right)\right)^2=\left(4x\right)^2=16x^2\)

b) ta có : \(\left(x+2\right)^3+\left(x-2\right)^3+x^3-3x\left(x+2\right)\left(x-2\right)\)

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

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

\(=2x^3-9x\left(x+2\right)\left(x-2\right)=2x^3-9x\left(x^2-4\right)\)

\(=2x^3-9x^3+36x=36x-7x^3\)

Answer 2

a) \(\left(2x+3\right)^2+\left(2x-3\right)^2-2\left(4x^2-9\right)\)

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

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

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

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

\(=6^2\)

\(=36\)

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

\(=x^3+3x^22+3x2^2+2^3+x^3-3x^22+3x2^2-2^3+x^3-3x\left(x^2-2^2\right)\)

\(=2x^3+2.3x2^2+x^3-3x^3+3x2^2\)

\(=24x+12x\)

\(=36x\)

Answer 3

Kết quả sẽ như sau nhé:

a, = 2x^2 + 2x + 9 + 2x^2 -12x + 9 -8x^2 + 18
= (2x^2 + 2x^2) + (12x-12x) + (9+9+18)

= -4x^2 + 36 (Kết quả)

b, = (x^3 + 6x^2 +12x+8+x^3 - 6x^2+12x - 8+x^3 -3x-x^2 -2^2

= (x^3+x^3+x^3) + (6x^2 -6x^2-x^2) + (12x+12x-3x) + (8-8-4)

= 3x^3 - x^2 + 21x - 4 (kết quả)

Nhớ bình chọn cho mình nha
Chúc bạn học tốt