$a-x+x-a+x-a+2x\\=a-a-a-x+x+x+2x\\=-a+3x$

$2xy-y+a+2y+y^2\\=y^2-y+2y+2xy+a\\=y^2+y+2xy+a$

$-14a-(-7+2a)\\=-14a+7-2a\\=-16a+7$

$-14a-(7-2a)\\=-14a-7+2a\\=-12a-7$

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

$2x(3x\cdot1)\\=6x^2$

$x^3\cdot x^7\\=x^{3+7}\\=x^{10}$

$(-1)\cdot\left(x^3\right)^2\\=(-1)\cdot x^{3\cdot2}\\=(-1)\cdot x^6\\=-x^6$

$\left(-x^3\right)^2\\=((-1)\cdot x^3)^2\\=(-1)^2\cdot(x^3)^2\\=1\cdot x^{3\cdot2}\\=x^6$

$\left(3x-1\right)\left(5x^2-2x\right)\\=15x^3-6x^2-5x^2+2x\\=15x^3-11x^2+2x$

$\left(uv-w^2\right)\left(uw+v^2\right)\\=u^2vw+uv^3-uw^3-w^2v^2$

$(x+1)(x-2)(x+3)\\=(x^2-2x+x-2)(x+3)\\=\left(x^2-x-2\right)\left(x+3\right)\\=x^3-x^2-2x+3x^2-3x-6\\=x^3-x^2+3x^2-2x-3x-6\\=x^3+2x^2-5x-6$

$7x^2-\left[x-x\left(3x+1\right)\right]\\=7x^2-\left(x-3x^2-x\right)\\=7x^2-\left(-3x^2\right)\\=7x^2+3x^2\\=10x^2$

$\left(3a+b\right)^2\\=\left(3a\right)^2+2\cdot3a\cdot b+b^2\\=9a^2+6ab+b^2$

$\left(\frac23-a\right)^2\\=\frac49-\frac43a+a^2$

$\left(\frac23a\right)^2\\=\frac 49a^2$

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

$10\left(x-\frac25\right)^3-0{,}8\left(6x-0{,}8\right)\\=10\left(x-\frac25\right)\left(x^2-\frac45x+\frac4{25}\right)-0{,}8\left(6x-0{,}8\right)\\=\left(10x-4\right)\left(x^2-\frac45x+\frac4{25}\right)-4{,}8x+0{,}64\\=10x^3-8x^2+\frac85x-4x^2+\frac{16}5x-\frac{16}{25}-4{,}8x+0{,}64\\=10x^3-8x^2-4x^2+\frac85x+\frac{16}5x-4{,}8x-\frac{16}{25}+0{,}64\\=10x^3-12x^2$