Question

How do you multiply $ \left( {2a + 3b + 4c} \right)$ with $-1$?

Answer 1

Hint: In the given question, we need to multiply $ \left( {2a + 3b + 4c} \right)$ with $-1$. $2a + 3b + 4c$ is an algebraic expression. An algebraic expression in mathematics is an expression which is made up of variables and constants.
There are three main types of algebraic expressions:
1. Expression with one term is called a monomial.
2. Expression with two unlike terms is called a binomial.
3. Expression with three unlike terms is called a trinomial.
The given expression is a trinomial expression. A trinomial is an algebraic expression that has three non zero terms. The given expression is $ - 1 \times \left( {2a + 3b + 4c} \right)$. So, here we need to multiply the trinomial expression with $ - 1$. We will use basic calculations to simplify expression.

Complete step by step answer:
Given $ - 1 \times \left( {2a + 3b + 4c} \right)$
On multiplying these two expressions,
$ \Rightarrow - 1 \times 2a - 1 \times 3b - 1 \times 4c$
On Simplification, we get
$ \Rightarrow - 2a - 3b - 4c$
Therefore, on multiplication of $ \left( {2a + 3b + 4c} \right)$ with $-1$, we get $ - 2a - 3b - 4c$.

Note:
To solve this type of questions, one must know how to multiply terms with opposite signs and same signs. While taking the product of two numbers, always keep in mind that product one positive and one negative number is always negative, product of two negative numbers is positive and product of two positive numbers is positive. To solve the questions based on algebraic expression, one must also know that the sum (or difference) of two like terms is a like term with coefficients equal to the sum (or difference) of coefficients of the two like terms. When we add (or subtract) two algebraic expressions, the like terms are added (or subtracted) and the unlike terms are written as they are.