Mathematics

Grade6

Easy

Question

# If a = 10, b = 20 and c = 5, then what is the value of (ab + ba + ca) (a + b + c)

- 15,750
- 1225
- 122
- 0

Hint:

### This is an algebraic expression. An algebraic expression consists of two components: a variable and a constant. A variable is a quantity that doesn't have a fixed value. It takes value as per the given conditions. It is generally denoted by an alphabet. A constant is a quantity with a fixed value. In this question, the variable is assigned some value. We have to substitute the given value in the above equation and then we have to perform the given operation. After performing all the given operations we will get the final value.

## The correct answer is: 15,750

### The given expression is:

(ab+ba+ca) (a+b+c) ... (1)

n this question, the variables are assigned some value. We have to substitute the values in the above expression to find the final value.

There are three different variables in the above expression. They are a, b, and c. The values of a = 10, b = 20, and c = 5. We have to be careful about the operations between the different variables.

Let's first consider the first bracket: (ab+ba+ca). There are three terms in this expression. Each of the terms ab, ba, and ca implies multiplication between two variables. After substituting the respective values, we get the following equation:

(ab+ba+ca) = [(10)(20)+(20)(10)+(5)(10)]

(ab+ba+ca) =(200+200+50)

(ab+ba+ca) =(450) ...(2)

Now let's take the second bracket: (a+b+c). There are single variables in this expression. We just have to substitute the given values and perform addition. After substituting the values, the expression becomes:

(a+b+c) = (10+20+5)

(a+b+c) = (35) ...(3)

Now, substituting (2) and (3) in the expression (1)

We get,

(ab+ba+ca) (a+b+c) = (450)(35)

(ab+ba+ca) (a+b+c) = (15750)

Therefore, option (a), which is '15750' is the right answer.

+b+c)

We have to be careful about the variables and operation between them.