Simplify the following expression with the use of distributive property-

$15\times 35+5\times 45$=?

(a) 750
(b) 650
(c) 350
(d) 700

Hint: Distributive property involves using of the following property-

a$\times $(b+c) = (a$\times $b)+(a$\times $c)

Where; a, b and c are numbers. Thus, we make use of this property to solve the given question.

Complete step-by-step answer:
We first try to understand the meaning of distributive property. According to the distributive property, multiplying the sum of two or more numbers by another number (say a) will give the same result as multiplying each number individually by that number (that number refers to number a) and then adding the products together. Thus, suppose we have two numbers, b and c. Now, according to the definition –

a$\times $(b+c) = (a$\times $b)+(a$\times $c) -- (1)

Thus, in this case, we have,

=$15\times 35+5\times 45$ -- (A)

Thus, here we have to make use of the inverse of the distributive property definition in (1). That is,

 (a$\times $b)+(a$\times $c) = a$\times $(b+c) -- (2)

Solving (A),

=$15\times 35+5\times 15\times 3$

(Since, 45 = $15\times 3$)

=$15\times 35+15\times 15$

(Since, $5\times 3$=15)

Now, we use the property (2), with a=15, b=35 and c=15. Thus, we have,

= 15$\times $(35+15)

=15$\times $50

=750

Hence, the correct answer is (a) 750.


Note: When solving a question related to distributive property, always think of simplifying the expression by breaking it down into its multiples. For example, in the above problem,$15\times 35+5\times 45$, we break down 45 since we can write 45 = $15\times 3$ and thus making it possible to use the distributive property.