Question

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

Answer 1

Hint: We use the distributive property of multiplication over addition \[a \times (b + c) = a \times b + a \times c\] to write the distribution of the term given in the question. We write the second number by breaking it into two parts.
* Distributive property is the property that helps to break the multiplication of large numbers into the sum of multiplication of smaller numbers. We distribute the large number into two or more parts and then multiply the number outside the bracket to each of the distributed parts.

Complete step-by-step answer:
We know the distributive property of multiplication over addition is given by \[a \times (b + c) = a \times b + a \times c\].
We have to use distributive property on the term \[258 \times 1008\] … (1)
To use the distributive property we have to write one of the numbers from the product as a sum of 2 numbers.
We can write \[1008 = 1000 + 8\]
Substitute the value of \[1008 = 1000 + 8\] in equation (1)
\[ \Rightarrow 258 \times 1008 = 258 \times (1000 + 8)\]
Comparing the RHS of the equation with distributive property \[a \times (b + c) = a \times b + a \times c\], we can write \[a = 258,b = 1000,c = 8\]
Therefore, substituting the values of a, b and c in RHS of the distributive property we get:
\[ \Rightarrow 258 \times (1000 + 8) = 258 \times 1000 + 258 \times 8\]
Therefore, the value of \[258 \times 1008\] from a distributive property is \[258 \times 1000 + 258 \times 8\].

So, the correct answer is “Option B”.

Additional Information: The distributive property is helpful in solving the algebraic expressions as they make the solution easier when complex and large algebraic terms are distributed in a simpler form.
Example: \[4{x^2}(1005x) = 4{x^2} \times (1000x + 5x)\]
Using the distributive property we can write
\[ \Rightarrow 4{x^2}(1005x) = 4{x^2} \times 1000x + 4{x^2} \times 5x\]
Doing multiplication of separate terms on RHS
\[ \Rightarrow 4{x^2}(1005x) = 4000{x^3} + 20{x^3}\]
Add the terms in RHS
\[ \Rightarrow 4{x^2}(1005x) = 4020{x^3}\]

Note: Students might try to break the first term i.e. \[258 = 250 + 8\] which can be a case but looking at the options we see that there is no breaking of first term, so we break the second term as that matches the options.