Addition and subtraction of polynomials

$4(x+6)+3(2+x+3x^2)-2x^2$

$7(x+x^3)-4x^3-x+1+4(x^2-2x^3+7)$

$5(a+2)+6a-7+(8+4)(a+3a+2)$

$x(x+3)+4x^2+2x$

$a^3(a^2+a+5)+a(a^4+3a^2+4)+1$

$2[8-3(x-3)]$

$x^2+3x+7[x+4x^2+3(x+x^2)]$

$x+3x$

$4x+7x$

$9a+12a$

$5m-3m$

$10x-7x$

$7y-9y$

$6k-11k$

$3a+5a+2a$

$9y+10y+2y$

$5m-7m-2m$

$h-3h-5h$

$a+8a+3a$

$7ab+4ab$

$8ax+2ax+6ax$

$3a^2+6a^2+2a^2$

$14a^{2}b+4a^{2}b+19a^{2}b$

$10y-15y$

$7ab-9ab+4ab$

$\begin{array}{cc}210a{b}^4+412a{b}^4+100a^{4}b& (\text{Look}\text{closely}\text{at}\text{the}\text{exponents.})\end{array}$

$\begin{array}{ccc}5x^2{y}^0+3x^{2}y+2x^{2}y+1,& y\ne 0& (\text{Look}\text{closely}\text{at}\text{the}\text{exponents.})\end{array}$

$8w^2-12w^2-3w^2$

$6xy-3xy+7xy-18xy$

$7x^3-2x^2-10x+1-5x^2-3x^3-12+x$

$21y-15x+40xy-6-11y+7-12x-xy$

$1x+1y-1x-1y+x-y$

$5x^2-3x-7+2x^2-x$

$-2z^3+15z+4z^3+z^2-6z^2+z$

$18x^{2}y-14x^{2}y-20x^{2}y$

$-9w^5-9w^4-9w^5+10w^4$

$2x^4+4x^3-8x^2+12x-1-7x^3-1x^4-6x+2$

$17d^{3}r+3d^{3}r-5d^{3}r+6d^{2}r+d^{3}r-30d^{2}r+3-7+2$

$\begin{array}{cc}{a}^0+2a^0-4a^0,& a\ne 0\end{array}$

$\begin{array}{cc}4x^0+3x^0-5x^0+7x^0-x^0,& x\ne 0\end{array}$

$\begin{array}{cc}2a^3{b}^{2}c+3a^2{b}^2{c}^0+4a^2{b}^2-a^3{b}^{2}c,& c\ne 0\end{array}$

$3z-6z+8z$

$3z^2-z+3z^3$

$6x^3+12x+5$

$3(x+5)+2x$

$7(a+2)+4$

$y+5(y+6)$

$2b+6(3-5b)$

$5a-7c+3(a-c)$

$8x-3x+4(2x+5)+3(6x-4)$

$2z+4ab+5z-ab+12(1-ab-z)$

$(a+5)4+6a-20$

$(4a+5b-2)3+3(4a+5b-2)$

$(10x+3y^2)4+4(10x+3y^2)$

$2(x-6)+5$

$1(3x+15)+2x-12$

$1(2+9a+4a^2)+a^2-11a$

$1(2x-6b+6a^{2}b+8b^2)+1(5x+2b-3a^{2}b)$

After observing the following problems, can you make a conjecture about $1(a+b)$ ?
$1(a+b)=$

Using the result of problem 52, is it correct to write
$(a+b)=a+b?$

$3(2a+2a^2)+8(3a+3a^2)$

$x(x+2)+2(x^2+3x-4)$

$A(A+7)+4(A^2+3a+1)$

$b(2b^3+5b^2+b+6)-6b^2-4b+2$

$4a-a(a+5)$

$x-3x(x^2-7x-1)$

$ab(a-5)-4a^{2}b+2ab-2$

$xy(3xy+2x-5y)-2x^2{y}^2-5x^{2}y+4x{y}^2$

$3h[2h+5(h+2)]$

$2k[5k+3(1+7k)]$

$8a[2a-4ab+9(a-5-ab)]$

$6\{m+5n[n+3(n-1)]+2n^2\}-4n^2-9m$

$5[4(r-2s)-3r-5s]+12s$

$8\{9[b-2a+6c(c+4)-4c^2]+4a+b\}-3b$

$5[4(6x-3)+x]-2x-25x+4$

$3x{y}^2(4xy+5y)+2x{y}^3+6x^2{y}^3+4y^3-12x{y}^3$

$9a^3{b}^7(a^3{b}^5-2a^2{b}^2+6)-2a(a^2{b}^7-5a^5{b}^{12}+3a^4{b}^9)-a^3{b}^7$

$-8(3a+2)$

$-4(2x-3y)$

$-4x{y}^2[7xy-6(5-x{y}^2)+3(-xy+1)+1]$

( [link] ) Simplify ${\left(\frac{x^{10}{y}^8{z}^2}{x^2{y}^6}\right)}^3$ .

( [link] ) Find the value of $\frac{-3(4-9)-6(-3)-1}{2^3}$ .

( [link] ) Write the expression $\frac{42x^2{y}^5{z}^3}{21x^4{y}^7}$ so that no denominator appears.

( [link] ) How many $(2a+5)\text{'}\text{s}$ are there in $3x(2a+5)$ ?

( [link] ) Simplify $3(5n+6m^2)-2(3n+4m^2)$ .