Question

How do you simplify $-5\left( 3x-7 \right)$?

Answer 1

The expression given in the above question, which is written as $-5\left( 3x-7 \right)$, consists of the multiplication of a number with a binomial. Therefore, in order to simplify the expression given in the above question, we need to apply the distributive rule of the algebraic multiplication, which is given by $a\left( b+c \right)=ab+ac$. By doing so and on further simplifying the expression obtained, we will obtain the final simplified form of the given equation.

Complete step by step solution:
Let us write the expression given in the above question as
$\Rightarrow E=-5\left( 3x-7 \right)$
In the above expression, we can see that there is a constant number, equal to $5$, which is being multiplied with the monomial $\left( 3x-7 \right)$. Therefore, for simplifying the above expression, we need to use the algebraic multiplication rule. The rule suitable for the simplification of the above expression is the distributive rule of the algebraic multiplication, which is given as $a\left( b+c \right)=ab+ac$. On comparing this rule with the above expression, we get $a=-5$, $b=3$, and $c=-7$. Therefore, on substituting these in the expression $a\left( b+c \right)=ab+ac$, we can simplify the above expression as
$\begin{aligned} & \Rightarrow E=-5\left( 3x \right)-5\left( -7 \right) \\\ & \Rightarrow E=-15x+35 \\\ \end{aligned}$
Hence, the given expression, which is given in the above question as $-5\left( 3x-7 \right)$, has been finally simplified as $-15x+35$.

Note: For solving these types of questions, we must be familiarized with the different algebraic properties, like the associative property, distributive property etc. We must not be confused by the names of these properties; instead one must be convenient in the application of these.