Ta luôn có \(a^2+b^2-2ab=\left(a-b\right)^2\)

Áp dụng hằng đẳng thức trên thì có :

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

\(=\left[\left(2x+5\right)-\left(2x+3\right)\right]^2\)

\(=2^2\)

\(=4\)

Nhầm

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

= (2x + 3 - 2x - 5)²

= (-2)²

= 4

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

= (2x + 3 + 2x + 5)²

= (4x + 8)²

= 16x² + 64x + 64

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

(2x+3)^2-(3x-5)^2+(2x+3)(2x-3)

= 4x^2 + 12x + 9 - (9x^2 - 30x + 25)  + 4x^2 - 9

= 8x^2 + 12x - 9x^2 + 30x - 25

= 42x - x^2 - 25

\(\left(2x+3\right)^2-\left(3x-5\right)^2+\left(2x+3\right)\left(2x-3\right).\)

\(=\left(4x^2+12x+9\right)-\left(9x^2-30x+25\right)+\left(4x^2-9\right)\)

\(=4x^2+12x+9-9x^2+30x-25+4x^2-9\)

\(=-x^2+42x-25\)

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

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

\(=\left[\left(2x+3\right)-\left(2x-5\right)\right]^2\)

\(=\left(2x+3-2x+5\right)^2=8^2=64\).

Merry Chrismas.

Bài 1:

a, \(\left(x-y+2z\right)^2=x^2+y^2+4z^2-2xy-4yz+4zx\)

b, \(\left(2x-3\right)\left(2x+3\right)\left(4x^2+9\right)=\left(4x^2-9\right)\left(4x^2+9\right)=16x^4-81\)

mình nhầm tí.

\(=\left(2x-3-2x-5\right)^2=\left(-8\right)^2=64\) nha

a: Ta có: \(\left(x+5\right)^2-4x\left(2x+3\right)^2-\left(2x-1\right)\left(x+3\right)\left(x-3\right)\)

\(=x^2+10x+25-4x\left(4x^2+12x+9\right)-\left(2x-1\right)\left(x^2-9\right)\)

\(=x^2+10x+25-16x^3-48x^2-36x-2x^3+18x+x^2-9\)

\(=-18x^3-46x^2-8x+16\)

Bài 6:

c: \(9x^2+6x+1=\left(3x+1\right)^2\)

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

e: \(x^3+27=\left(x+3\right)\left(x^2-3x+9\right)\)

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

`=6x^2-2x-2x^2+6x-x+3`

`=4x^2+3x+3`

2) `3(x^2-3x)-(4x+2)(x-1)`

`=3x^2-9x-4x^2+4x-2x+2`

`=-x^2-7x+2`

3) `3x(x-5)-(x-2)^2-(2x+3)(2x-3)`

`=3x^2-15x-(x^2-4x+4)-(4x^2-9)`

`=3x^2-15x-x^2+4x-4-4x^2+9`

`=-2x^2-11x+5`

4) `(2x-3)^2+(2x-1)(x+4)`

`=4x^2-12x+9+2x^2+8x-x-4`

`=6x^2-5x+5`

\(=4x^2+6x-10x-15-4x^2+4x-1=-16\)