Question

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

Answer 1

Hint:This problem uses the standard identities of expansion. We know that, \[{\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}\]. So here in the problem above take $a=x$ and $b=4$. Then solve it using the formula of the identity.

Complete step by step answer:
Given that \[{\left( {x + 4} \right)^2}\]
Now taking the help of the identity above we can write,
\[{\left( {x + 4} \right)^2} = {x^2} + 2 \times x \times 4 + {4^2}\]
Taking the squares and multiplying the numbers in the middle term,
\[ {\left( {x + 4} \right)^2}= {x^2} + 8x + 16\]
This is the correct answer for the square of the bracket given above.
\[\therefore {\left( {x + 4} \right)^2} = {x^2} + 8x + 16\]

Hence, the simplified form of \[{\left( {x + 4} \right)^2}\] is \[{x^2} + 8x + 16\].

Note: the expansion sometimes can use minus sign instead of plus in the middle. So do carefully use the identity \[{\left( {a - b} \right)^2} = {a^2} - 2ab + {b^2}\]. Also, we can solve this by multiplying the bracket with itself because squaring is nothing but a product of the same number with itself. Note that squares of both positive as well as negative numbers are always positive.