Question

Using distributive property,\[258 \times 1008 = ?\]
A. \[258 + 1000 + 8\]
B. \[258 \times 1000 + 258 \times 8\]
C. \[258 \times 1000 + 8\]
D. \[1000 + 258 \times 8\]

Answer 1

Hint: In this question we have to choose the correct option to be the solution for the given relation. By using the definition of distributive property we get that multiplying a number by a group of numbers added together is the same as doing each multiplication separately.
To apply the distributive property, we change the number to its nearest tens or hundreds or thousands as per the given problem.

Formula used: Let us consider, \[a,b,c\] be three integers. Now, the distributive property states that:
\[a(b + c) = a \times b + a \times c\]

Complete step-by-step answer:
It is given that; \[258 \times 1008\]
We have to simplify it by using distributive property.
To “distribute” means to divide something or give a share or part of something.
According to the distributive property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
The Distributive Law says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately.
Let us consider, \[a,b,c\] be three integers. Now, the distributive property states that:
\[a(b + c) = a \times b + a \times c\] or, \[a(b - c) = a \times b - a \times c\]
To apply the distributive property, we change the number to its nearest tens or hundreds or thousands as per the given problem.
Here, \[1008\] is closer to \[1000\]. So, \[1008\] can be written as \[1000 + 8\].
So, the given problem can be written as,
\[ \Rightarrow 258 \times 1008 = 258 \times (1000 + 8)\]
Now we will apply distributive property.
Substitute \[a = 258,{\text{ }}b = 1000,{\text{ }}c = 8\] in the general formula of the distributive property we get,
\[ \Rightarrow 258 \times 1000 + 258 \times 8\]
Hence, the correct answer is \[258 \times 1000 + 258 \times 8\]

So, the correct answer is “Option B”.

Note: The distributive property, sometimes known as the distributive property of multiplication, tells us how to solve certain algebraic expressions that include both multiplication and addition.
The literal definition of the distributive property is that multiplying a number by a sum is the same as doing each multiplication separately.
Distributive property does not satisfy division and addition.