Question

How do you simplify \[-5\left( 2x+4 \right)\]?

Answer 1

Hint: Given is the simple linear expression in one variable, we can simplify it by expanding the bracket. To simplify the expression, we have to use the distributive property of the algebra which states that, the expressions of the form \[a(b+c)\] are simplified by multiplying the term outside the bracket with the terms inside the brackets and adding their products. Algebraically it is expressed as \[a(b+c)=ab+ac\]

Complete step by step solution:
We are asked to simplify the expression \[-5\left( 2x+4 \right)\]. We can see that this expression is of the form \[a(b+c)\]. Here, we have a, b, c as \[-5,2x,4\] respectively. We know to expand these expressions; we have to use the distributive property.
By using the distributive property we get, \[a(b+c)=ab+ac\]
Substituting the values of the a, b, and c we get
\[\Rightarrow -5\left( 2x+4 \right)\]
\[\Rightarrow -5\left( 2x \right)-5\times 4\]
By multiplying 5 and 2 we get 10, and by multiplying 5 and 4 we get 20. Substituting these values in the above expansion, we get
\[\Rightarrow -10x-20\]
This is the simplified form of the given expression.

Note:
To simplify expressions of these forms, we should know the expansions of different algebraic expressions. Some of the expansions we should know are \[a(b+c)=ab+ac\], \[\left( c+d \right)\left( a+b \right)=ca+cb+da+db\].
These types of expressions are common while solving equations in one or many variables. So, their expansions are important to remember.
For example, we can convert the given expression into an equation as \[-5\left( 2x+4 \right)=0\]. To solve this equation, we have to simplify it first, and then solve it to find the solution for x.