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**Hint:**In order to multiply $ - 5\left( {3x - 7} \right)$, we will use distributive law i.e., $P\left( {X + Y} \right) = PX + PY$. By comparing the distributive law with the given term, we will substitute the values and determine the required value.

**Complete step-by-step solution:**

Now, we need to multiply $ - 5\left( {3x - 7} \right)$.

We can use the distributive property here, to multiply $ - 5\left( {3x - 7} \right)$.

The distributive property states that when a factor is multiplied by the sum of two terms, it is essential to multiply each of the two numbers by the factor, and finally perform the addition operation.

$P\left( {X + Y} \right) = PX + PY$

Thus, $ - 5\left( {3x - 7} \right) = - 5\left( {3x} \right) + \left( { - 5} \right)\left( { - 7} \right)$

Hence, $ - 5\left( {3x - 7} \right) = - 15x + 35$

**Note:**To “distribute” means to divide something or give a share or part of something. The distributed property helps in making difficult problems simpler. We can use the distributive property of multiplication to rewrite expression by distributing or breaking down a factor as a sum or difference of two numbers. Even though division is the inverse of multiplication, the distributive law only holds true in case of division, when the dividend is distributed or broken down.

The distributive property is an algebraic property that is used to multiply a single value and two or more values within a set of parenthesis. In propositional logic, distribution refers to two valid rules of replacement. The rules allow one to reformulate conjunctions and disjunctions within logical proofs.

The distributive property of multiplication can be expressed under addition and subtraction. The operation exists inside the bracket, between the numbers. The distributive property of division can divide larger numbers using the distributive property by breaking those numbers into smaller factors.

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