Question

How do you simplify ${\left( { - 3x} \right)^2}$?

Answer 1

Hint:
Here we must know the property of multiplication that when we have the term of the form ${\left( {ab} \right)^n}$ then we can simplify it and write this in the form of ${a^n}{b^n}$ and in the similar way we can write the above given term and find the value required after simplification.

Complete step by step solution:
Here we are given to simplify ${\left( { - 3x} \right)^2}$ which means we need to find its value till we cannot further simplify the term.
So we know that when we have the term of the form ${\left( {ab} \right)^n}$ then we can simplify it and write this in the form of ${a^n}{b^n}$
Now here we have the term ${\left( { - 3x} \right)^2}$
So we can write it as ${\left( {( - 1)(3)(x)} \right)^2}$
Now we have the form as ${\left( {abc} \right)^n}$ which can be simplified as ${a^n}{b^n}{c^n}$
So if we compare ${\left( {abc} \right)^n}$ with the term ${\left( {( - 1)(3)(x)} \right)^2}$ we will get that:
$
  a = - 1 \\
  b = 3 \\
  c = x \\
  n = 2 \\
 $
Hence we will get the simplified form as:
${\left( {( - 1)(3)(x)} \right)^2}$
${( - 1)^2}{(3)^2}{(x)^2}$$ - - - (1)$
Now we need to find the square of the numbers as the power is $2$
We know that the square of the number is found by finding the product of the number with itself. For example square of the number $1 = (1)(1) = 1$
Similarly here we need to find the square of $ - 1 = {\left( { - 1} \right)^2} = 1$
Square of $3 = {\left( 3 \right)^2} = 9$
Square of $x = {x^2}$
So we can now substitute the value of all the squares in the equation (1) and get the term as:
${( - 1)^2}{(3)^2}{(x)^2}$
$(1)(9){x^2}$
So we can multiply here $1{\text{ and 9}}$ and get the result after multiplication as:
${\left( { - 3x} \right)^2}$$ = $$9{x^2}$

Note:
Here the student makes the error here by squaring only the variable term which is $x$ but he must know that when we need to square such term we need to take the square of each and every term inside the bracket.