Question

How do you find the sum or difference of \[\left( {2x + 3{x^2}} \right) - \left( {7 - 8{x^2}} \right)\] ?

Answer 1

Hint: A combination of variables, constants, and operators constitute an algebraic expression. The sum is the result of adding two or more numbers. The difference of two numbers is the result of subtracting these two numbers. Addition and subtraction of algebraic expressions are almost similar to the addition and subtraction of numbers. But here in the given algebraic expressions, like terms and unlike terms must be sorted together, then we need to apply distributive property and evaluate the terms to get the equation.

Complete step by step solution:
Given,
 \[\left( {2x + 3{x^2}} \right) - \left( {7 - 8{x^2}} \right)\]
Apply distributive property to the second half terms, as:
 \[ \Rightarrow \left( {2x + 3{x^2}} \right) + \left[ { - 1 \cdot \left( {7 - 8{x^2}} \right)} \right] \]
Multiplying the second half terms, we get:
 \[ \Rightarrow \left( {2x + 3{x^2}} \right) + \left[ { - 1\left( 7 \right) + \left( { - 1} \right)\left( { - 8{x^2}} \right)} \right] \]
Simplifying the terms, we get:
 \[ \Rightarrow \left( {2x + 3{x^2}} \right) + \left[ { - 7 + 8{x^2}} \right] \]
Now, remove parentheses and change signs where needed:
 \[ \Rightarrow 2x + 3{x^2} - 7 + 8{x^2}\]
 Add the like terms as:
 \[ \Rightarrow 2x + 11{x^2} - 7\]
Now, reorder to quadratic format we have:
 \[ \Rightarrow 11{x^2} + 2x - 7\]
Therefore, sum or difference of \[\left( {2x + 3{x^2}} \right) - \left( {7 - 8{x^2}} \right) = 11{x^2} + 2x - 7\] .
So, the correct answer is “$11{x^2} + 2x - 7$”.

Note: For adding two or more algebraic expressions the like terms of both the expressions are grouped together. The coefficients of like terms are added together using simple addition techniques and the variable which is common is retained as it is. The, unlike terms, are retained as it is and the result obtained is the addition of two or more algebraic expressions.To solve the given expression, the knowledge of like and unlike terms is crucial while studying addition and subtraction of algebraic expressions because the addition and subtraction of numbers can only be performed on like terms. The terms whose variables and their exponents are the same are known as like terms and the terms having different variables are unlike terms.