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

(x² + 1)(x - 3) - (x - 3)(x² - 1)
= [x² + 1 - (x² - 1)](x - 3)

= (x² + 1 - x² + 1)(x - 3)

= 2(x - 3)

`=(x-3)[x^2+1-(x^2-1)]`

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

`=2(x-3)`

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

\(=9x^2-30x+25+x^2+4x+4+3x-4x^2\)

\(=6x^2-23x+29\)

\(=25-30x+9x^2+x^2+4x+4+3x-12x^2=-2x^2-23x+29\)

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

\(=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)

\(=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)

\(=x^3-16x^2+25x\)

\(=x^3-27-4x^2+4x-1=x^3-4x^2+4x-28\)

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

\(=x^2-2x+1-\left(x+2\right)\left[2x-4+3\left(x^2+4x+4\right)\right]\)

\(=x^2-2x+1-\left(x+2\right)\left(3x^2+14x+8\right)\)

\(=x^2-2x+1-\left(3x^3+6x^2+14x^2+28x+8x+16\right)\)

\(=-3x^3-21x^2-38x-15\)

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

\(=x^3+2x^2+4x-2x^2-4x-8\) \(-\left(x^3-3x^2.3+3x.3^2-27\right)-\)-\(\left(x^3-3.x^2.2+3.x.2^2-8\right)\)

\(=x^3-8\) \(-x^3+9x^2-27x+27-x^3+6x^2-12x+8\)

\(=-x^3+15x^2-39x+27\)

học tốt

a: \(\left(x-2y\right)^2+\left(x-\dfrac{1}{2}y\right)\left(x+\dfrac{1}{2}y\right)\)

\(=x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2\)

\(=2x^2-4xy+\dfrac{15}{4}y^2\)

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

\(=x^2-4x+4+x^2+6x+9-2\left(x^2-1\right)\)

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

=2x+15

a) \(=x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2=2x^2-4xy+\dfrac{15}{4}y^2\)

b) \(=x^2-4x+4+x^2+6x+9-2x^2+2\)

\(=2x+15\)

a; \(\left(x-2y\right)^2+\left(x-\dfrac{1}{2}y\right)\left(x+\dfrac{1}{2}y\right)\)

= \(x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2\)

= \(2x^2-4xy+\dfrac{15}{4}y^2\)

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

= \(x^2-4x+4+x^2+6x+9-2x^2+2\)

= \(2x+15\)

Bài làm:

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

\(=2x^2+x-10-3\left(x^2+4x+4\right)+x^2+2x+1\)

\(=3x^2+3x-9-3x^2-12x-12\)

\(=-9x-21\)

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

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

\(=2x^2-4x+5x-10-3x^2-12x-12+x^2+2x+1\)

\(=\left(2x^2-3x^2+x^2\right)+\left(5x-4x-12x+2x\right)-\left(10+12-1\right)\)

\(=0+x-10x-21=-9x-21\)

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

\(=2x^2-4x+5x-10-3x^2-12x-12+x^2+2x+1\)

\(=-9x-21\)