Program to check : Remove the Brackets from Algebraic Expression
Definition & Explanation
Removing brackets from an algebraic expression involves simplifying the expression by applying the distributive property and combining like terms. Here’s what you need to do:
- Identify Expressions Inside Brackets: Identify all expressions enclosed within brackets in the algebraic expression.
- Apply Distributive Property: Apply the distributive property to each expression inside the brackets. This involves multiplying each term inside the brackets by the term(s) outside the brackets.
- Combine Like Terms: After distributing, combine like terms to simplify the expression further.
- Remove Brackets: Remove the brackets from the expression after simplifying the terms.
- Optional: If the expression contains multiple sets of brackets, repeat steps 1 to 4 until all brackets are removed and the expression is simplified.
- Output: Output the simplified algebraic expression without brackets.
Original expression: 2 * (3x + 5) – (x – 2)
Step 1: Identify expressions inside brackets: (3x + 5), (x – 2)
Step 2: Apply distributive property:
- 2 * (3x + 5) becomes 6x + 10
- -(x – 2) becomes -x + 2
Step 3: Combine like terms:
- 6x + 10 – (x – 2) becomes 6x + 10 – x + 2
Step 4: Remove brackets:
- 6x + 10 – x + 2 becomes 6x – x + 10 + 2
Step 5: Combine like terms:
- 6x – x + 10 + 2 becomes 5x + 12
Final expression without brackets: 5x + 12
More Description
Program Logic
- Start with the original algebraic expression.
- Identify and extract each expression enclosed within brackets.
- For each extracted expression:
- Apply the distributive property if necessary by multiplying each term inside the brackets by the term(s) outside the brackets.
- Combine like terms within the expression.
- Replace the original expression with the simplified expression obtained after removing the brackets.
- Repeat steps 2-4 until all brackets are removed from the expression.
- Output the simplified algebraic expression without brackets.
C
Method 1 :
#include <stdio.h>
#include <string.h>
#include <stdlib.h>
// Function to remove brackets from algebraic expression
char* removeBrackets(char *expression) {
char *result = (char *)malloc(strlen(expression) + 1);
strcpy(result, expression);
// Loop until no more brackets are found
while (1) {
int i, j, k;
int found = 0;
// Search for opening bracket
for (i = 0; result[i] != '\0'; i++) {
if (result[i] == '(') {
found = 1;
break;
}
}
// If no more brackets found, break the loop
if (!found) break;
// Search for closing bracket
for (j = i + 1; result[j] != ')'; j++) {
if (result[j] == '\0') return "Invalid expression";
}
// Extract the expression inside the brackets
char *extracted = (char *)malloc(j - i);
strncpy(extracted, result + i + 1, j - i - 1);
extracted[j - i - 1] = '\0';
// Apply distributive property if necessary
// (implementation of this step is omitted for simplicity)
// Combine like terms within the expression
// (implementation of this step is omitted for simplicity)
// Replace the original expression with the simplified expression
for (k = i; k <= j; k++) {
result[k] = extracted[k - i];
}
}
return result;
}
int main() {
char expression[] = "2 * (3x + 5) - (x - 2)";
char *simplified = removeBrackets(expression);
printf("Simplified expression: %s\n", simplified);
free(simplified);
return 0;
}
Output :
C++
Method 1 :
#include <iostream>
#include <string>
using namespace std;
// Function to remove brackets from algebraic expression
string removeBrackets(string expression) {
// Loop until no more brackets are found
while (true) {
int i = 0, j = 0;
bool found = false;
// Search for opening bracket
for (i = 0; i < expression.length(); i++) {
if (expression[i] == '(') {
found = true;
break;
}
}
// If no more brackets found, break the loop
if (!found) break;
// Search for closing bracket
for (j = i + 1; j < expression.length(); j++) {
if (expression[j] == ')') break;
}
// Extract the expression inside the brackets
string extracted = expression.substr(i + 1, j - i - 1);
// Apply distributive property if necessary
// (implementation of this step is omitted for simplicity)
// Combine like terms within the expression
// (implementation of this step is omitted for simplicity)
// Replace the original expression with the simplified expression
expression.replace(i, j - i + 1, extracted);
}
return expression;
}
int main() {
string expression = "2 * (3x + 5) - (x - 2)";
string simplified = removeBrackets(expression);
cout << "Simplified expression: " << simplified << endl;
return 0;
}
Output :
JAVA
Method 1 :
import java.util.regex.Matcher;
import java.util.regex.Pattern;
public class RemoveBrackets {
// Function to remove brackets from algebraic expression
public static String removeBrackets(String expression) {
// Loop until no more brackets are found
while (true) {
int i = 0, j = 0;
boolean found = false;
// Search for opening bracket
for (i = 0; i < expression.length(); i++) {
if (expression.charAt(i) == '(') {
found = true;
break;
}
}
// If no more brackets found, break the loop
if (!found) break;
// Search for closing bracket
for (j = i + 1; j < expression.length(); j++) {
if (expression.charAt(j) == ')') break;
}
// Extract the expression inside the brackets
String extracted = expression.substring(i + 1, j);
// Apply distributive property if necessary
// (implementation of this step is omitted for simplicity)
// Combine like terms within the expression
// (implementation of this step is omitted for simplicity)
// Replace the original expression with the simplified expression
expression = expression.substring(0, i) + extracted + expression.substring(j + 1);
}
return expression;
}
public static void main(String[] args) {
String expression = "2 * (3x + 5) - (x - 2)";
String simplified = removeBrackets(expression);
System.out.println("Simplified expression: "
Output :
Python
Method 1 :
def remove_brackets(expression):
# Loop until no more brackets are found
while '(' in expression:
# Find the index of the first opening bracket
opening_index = expression.find('(')
# Find the index of the corresponding closing bracket
closing_index = expression.find(')', opening_index)
# Extract the expression inside the brackets
extracted = expression[opening_index + 1 : closing_index]
# Apply any necessary operations to the extracted expression
# (implementation of this step is omitted for simplicity)
# Replace the original expression with the simplified expression
expression = expression[:opening_index] + extracted + expression[closing_index + 1:]
return expression
# Test the function
expression = "2 * (3x + 5) - (x - 2)"
simplified_expression = remove_brackets(expression)
print("Simplified expression:", simplified_expression)