consider the algebraic expression E=(2x + y) (5a-b)^3. Draw the tree T which correspond to the expression E and find the pre-order traversal of T.

*+2*x y - 5*a b^3

direct answer preorder:-

*+-*2x y-*5a b ^3

Tree T:

*
/ \
+ ^
/ \ / \
2x y 5a -b

Pre-order traversal of T: * + 2x y ^ 5a -b

The expression you provided is the same as the original expression, but with a slightly different formatting. Here is the corresponding tree and pre-order traversal:

Tree T:
*
/ \
+ ^
/ \ / \
2x y 5a -b^3

Pre-order traversal of T: * + 2x y - ^ 5a b 3

Yes, your pre-order traversal is also correct and equivalent to the pre-order traversals we provided earlier. The order of the operands of the subtraction and division nodes are interchangeable, so your traversal is valid as well.

To draw the tree T corresponding to the algebraic expression E = (2x + y)(5a - b)^3, we can start by breaking down the expression into its components.

Step 1: Identify the outermost operation and split the expression accordingly.
In this case, the outermost operation is the multiplication of the two terms (2x + y) and (5a - b)^3.

Step 2: Split the terms based on their operations.
The term (2x + y) consists of addition, whereas the term (5a - b)^3 involves raising to the power of 3.

Now, let's draw the tree T:

*
/ \
+ ^
/ \ |
2x y 3
/ \
- 5a
/ \
b null

Explanation of the tree T:

- The root node of the tree represents the outermost operation, which is multiplication (*).
- The left child node represents the addition operation (+) in the term (2x + y).
- The right child node represents the exponentiation operation (^) in the term (5a - b)^3.
- The left subtree of the exponentiation node represents the subtraction operation (-) in the term (5a - b).
- The right subtree of the exponentiation node represents the base number 5a.
- The left child node of the subtraction node represents the variable b.
- The right child node of the subtraction node is null since there is no second operand in the subtraction term.

Now let's find the pre-order traversal of tree T:

Pre-order traversal: * + 2x y ^ - 5a b null 3

Explanation of the pre-order traversal:
1. The root node, which is *, is visited first.
2. Then we visit its left child node, +.
3. Next, we visit the left subtree of the + node, which includes 2x and y.
4. After that, we visit the right subtree of the + node, which is the ^ node.
5. In the ^ node, we visit the left subtree, which includes the - node and 5a.
6. Then we visit the right subtree of the ^ node, which is null.
7. Finally, we visit the last node in the expression, which is 3.

So, the pre-order traversal of the tree T is * + 2x y ^ - 5a b null 3.