Question

Simplify the expression \[3x\left( {4x - 5} \right) + 3\] and find its value for $ x = 3 $ ?

Answer 1

Hint: First of all we will break the bracket by multiplying $ 3x $ with the terms inside the bracket and we will convert it into three terms having one unknown variable that is $ x $ and after that we will add the similar terms and we will have a final value.
After this as we are given with the value $ x = 3 $ we will replace it in place of $ x $ and we will again operate the mathematical operation that is given, which is addition and subtraction in this case.

Complete step-by-step answer:
Here, the expression given in the question is:
\[3x\left( {4x - 5} \right) + 3\]
So, at first we will open the bracket by multiplying the value $ 3x $ with each term present inside the bracket.
So now at first we will multiply $ 3x $ with $ 4x $ then we will multiply $ 3x $ with $ 5 $ and we will subtract ( $ 3x \times 5 $ ) from ( $ 3x \times 4x $ ) and then we will add it with $ 3 $ .
 So, the resulting values are:
 $ 3x \times 4x = 12{x^2} $ -------(1)
And,
 $ 3x \times 5 = 15x $ ------(2)
 Now we need to subtract (2) from (1) and add it with 3
 \[12{x^2} - 15x + 3\] ------(3)
The above equation is the simplified version of the expression \[3x\left( {4x - 5} \right) + 3\]
Now we will put the value of $ x $ :
We are given that $ x = 3 $ .
Putting this value in (3) we get:
\[\Rightarrow 12{(3)^2} - 15 \times 3 + 3\]
\[ = 108 - 45 + 3\]
\[ = 66\]
So the final answer we got is 66.
Therefore, the simplified version of the expression \[3x\left( {4x - 5} \right) + 3\] is \[12{x^2} - 15x + 3\] and its value for $ x = 3 $ is $ 66 $

Note: While solving the equation we should take care of the sign or else we may get another value. And we take care while putting the value of the variable. Keep all the variables of the expression in a proper arrangement to avoid errors.