Question

Solve the question by using the distributive law \[375\times 999\]?

Answer 1

Hint: To solve this problem first of all, let us understand what a distributive law is. We are going to use the distributive law of multiplication over subtraction. You can write the 999 into (1000-1). Then we can apply the distributive law.

Complete step-by-step answer:
What is distribution law?
The Distributive law, in mathematics, the law relating the operations of multiplication and addition, stated symbolically, a (b + c) = ab + ac; that is, the monomial factor a is distributed, or separately applied, to each term of the binomial factor b + c, resulting in the product ab + ac. From this law it is easy to show that the result of first adding several numbers and then multiplying the sum by some number is the same as first multiplying each separately by the number and then adding the products.
In mathematics, distributive law is the law relating the operations of multiplication and subtraction, symbolically we can write it as a(b-c) =ab-ac i.e. the monomial factor a is distributed to each term of binomial factor. b-c, resulting in the product ab+ac from this law it is easy to show that the result of first subtracting several numbers and then multiplying the difference by the same number is the same as first multiplying each separately by the number and then subtracting the products.
Now, let us solve the given problem.
We have given \[375\times 999\]to solve by distributive law.
For this let us write 999 as 1000-1
999=1000-1
So, we have,
\[\begin{align}
  & 375\times 999 \\
 & =375\times \left( 1000-1 \right) \\
 & =375\times 1000-375\times 1 \\
 & =375000-375 \\
 & =374625 \\
\end{align}\]

Note: In the above solution, we have used a(b-c)=ab-ac because the problem is about expanding one term as a subtraction of two numbers. If we will be given expanding ne term as addition two numbers then we will use a(b+c)=ab+ac
And also we can solve this problem by this method also:
\[\begin{align}
  & 375\times 999=375\left( 1000-1 \right) \\
 & =375\times 1000-375 \\
 & =375000-375 \\
 & =374625 \\
\end{align}\]
By this method also we can solve this question still we get the same answer.