Question

How do we simplify \[{\left( {x + 4} \right)^2}\]?

Answer 1

Hint: In the given question, we have been given an algebraic expression. There is a variable and a constant inside a bracket and the whole bracket is squared. We have to simplify the value of the given expression. Clearly, that can be done by applying the formula of the whole square of two numbers.

Formula Used:
We are going to use the formula of whole square of two numbers, which is,
\[{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\]

Complete step-by-step answer:
The given expression is \[{\left( {x + 4} \right)^2}\].
To simplify the value of this expression, we are going to apply the formula of whole square of two numbers, which is,
\[{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\]
Hence, \[{\left( {x + 4} \right)^2} = {x^2} + 8x + 16\]

Additional Information:
In the given question, we applied the formula of the whole square of two numbers. But if there was a negative sign, and we had to evaluate the answer of difference, then the formula for that is,
\[{\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}\]

Note: In the given question, we had to evaluate the value of a given algebraic expression. We observed that the expression is a whole square and we just applied the relevant formula on the given expression and evaluated the answer.