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

$2xy-y+a+2y+y^2=y^2-y+2y+2xy+a=y^2+y+2xy+a2xy-y+a+2y+y^2\backslash \backslash =y^2-y+2y+2xy+a\backslash \backslash =y^2+y+2xy+a$

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

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

$2x(3x+1)=6x^2+2x2x(3x+1)\backslash \backslash =6x^2+2x$

$2x(3x\cdot 1)=6x^{2}2x(3x\backslash cdot1)\backslash \backslash =6x^2$

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

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

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

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

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

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

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

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

${(\frac{2}{3}-a)}^2=\frac{4}{9}-\frac{4}{3}a+a^2\backslash left(\backslash frac23-a\backslash right)^2\backslash \backslash =\backslash frac49-\backslash frac43a+a^2$

${\left(\frac{2}{3}a\right)}^2=\frac{4}{9}{a}^2\backslash left(\backslash frac23a\backslash right)^2\backslash \backslash =\backslash frac\; 49a^2$

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

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