First, distribute the negative sign into the parentheses.

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

Next, combine like terms.

\(\displaystyle x^3+9x^2-x-2\)

Note that all operations in this problem are addition and subtraction; there is no need to FOIL or multiply.

First, work from left to right completing multiplication and division, then work from left to right completing addition and subtraction. 

\(\displaystyle 17+(2\cdot 4)-(6/2)\)

\(\displaystyle 17+8-3=22\)

By order of operations, always carry out any operations within parentheses first; this is the addition.  This removes the parentheses; what remains is a square, a multiplication, and a division. Since there are no more grouping symbols, square next. The multiplication is done next, as multiplications and divisions are performed in left-to-right order.

In summary: Add, square, multiply, divide

By order of operations, always carry out any operations within parentheses first; this is the addition. This removes the parentheses; what remains is a square, a multiplication, and a subtraction. This is the correct order in the absence of grouping symbols.

In summary: Add, square, multiply, subtract

The order of operations is parenthesis, exponents, multiplication, division, addition, subtraction (PEMDAS).

\(\displaystyle 4+2x-1(5^2* 3)\)

First, we will evaluate the parentheses. Within the parentheses, we need to solve the exponent, then multiply,

\(\displaystyle 4+2x-1(25* 3)\)

\(\displaystyle 4+2x-1(75)\)

Now that the parenthesis is evaluated, we need to multiply.

\(\displaystyle 4+2x-75\)

Finally, we add and subtract. We can arrange the terms in any order.

\(\displaystyle 2x+4-75\)

\(\displaystyle 2x-71\)

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

\(\displaystyle 2\left \{ 3+2[1+(3-2)]\right \}\)

\(\displaystyle =2\left \{ 3+2[1+(1)]\right \}\)

\(\displaystyle =2\left \{ 3+2[2]\right \}\)

\(\displaystyle =2\left \{ 3+4\right \}\)

\(\displaystyle =2\left \{ 7\right \}\)

\(\displaystyle =14\)

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

\(\displaystyle 5+[2+3(3-2^2)]\)

\(\displaystyle =5+[2+3(3-4)]\)

\(\displaystyle =5+[2+3(-1)]\)

\(\displaystyle =5+[2+(-3)]\)

\(\displaystyle =5+[-1]\)

\(\displaystyle =4\)

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses: 

\(\displaystyle 6^2-[4+3(-6-1)]\)

\(\displaystyle =6^2-[4+3(-7)]\)

\(\displaystyle =6^2-[4+(-21)]\)

\(\displaystyle =6^2-[-17]\)

\(\displaystyle =36+17\)

\(\displaystyle =53\)

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

\(\displaystyle (3*2+1)-2[3-(4-2)]\)

\(\displaystyle =(6+1)-2[3-(2)]\)

\(\displaystyle =(7)-2[1]\)

\(\displaystyle =7-2\)

\(\displaystyle =5\)

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

\(\displaystyle 2^2[2+(3-4)]+[5(2+1-7)]\)

\(\displaystyle =2^2[2+(-1)]+[5(-4)]\)

\(\displaystyle =2^2[1]+[-20]\)

\(\displaystyle =4[1]+[-20]\)

\(\displaystyle =4-20\)

\(\displaystyle =-16\)