Question

Using distributive property to rewrite and evaluate: $\left( {4 + 6} \right)11$ .

Answer 1

Hint:The given problem requires us to use the distributive property to evaluate the algebraic product given to us. Distributive law is applicable for various scenarios and situations including multiplication over addition. There are various other algebraic properties just like the distributive property that help us to solve questions or problems involving algebraic operations and simplification.

Complete step by step solution:
Distributing something with someone means to share or give a part of a specific thing to them. 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 property of binary operations generalizes the distributive law from Boolean algebra and elementary algebra. In general, the distributive property can be represented as follows:
 \[\left( {a + b} \right)c = \left( {ac + bc} \right)\] .
Using the distributive property for evaluating the product given to us, we get,
$\left( {4 + 6} \right)11 = 4 \times 11 + 6 \times 11$
$\left( {4 + 6} \right)11 = 44 + 66$
$\left( {4 + 6} \right)11 = 110$
Hence, the answer for the given question can be calculated using the distributive law, and comes out to be $\left( {4 + 6} \right)11 = 110$ .
Note: There are many algebraic properties such as commutative property, distributive property, associative property and many more. Such properties are of significant use when we have to simplify an algebraic expression or an operation. In fact, these properties can be used to simplify trigonometric and calculus based problems and questions as well.