Question

How do you write ${(x + 4)^2}$ in standard form?

Answer 1

Hint: In this question, we are asked to write ${(x + 4)^2}$ in the standard form. To write a polynomial in a standard form, we need to simply and rearrange it in the form of $a{x^2} + bx + c$.
We need to split the term into two and then multiply it in FOIL method and arrange it in the form of $a{x^2} + bx + c$.

Complete step-by-step solution:
The given polynomial is ${(x + 4)^2}$, we have to write it in the standard form. In order to write any polynomial equation in a standard form we have to rearrange it in the form of $a{x^2} + bx + c$.
First we need to split the given polynomial ${(x + 4)^2}$
We know that we can write ${(x + 4)^2}$ as $(x + 4)(x + 4)$ .
By using FOIL method, we will find the value of $(x + 4)(x + 4)$
In algebra, FOIL is a standard method of multiplying two binomials and hence the method may be referred to as the FOIL method
The general formula is,
$(a + b)(c + d) = ac + ad + bc + bd$
Now, we can write it as,
$ \Rightarrow (x + 4)(x + 4) = {x^2} + 4x + 4x + 16$
On adding the variables, we get
$ \Rightarrow {x^2} + 8x + 16$
Now we need to change the resultant equation in the form of $a{x^2} + bx + c$
Here, the equation is already in the form $a{x^2} + bx + c$

Therefore, ${x^2} + 8x + 16$ is the standard form of the polynomial ${(x + 4)^2}$.

Note: In this question we have alternative way as follows,
There is a alternative method to find or expand the given polynomial using a very common most used formula ${\left( {a + b} \right)^2} = {a^2} + 2ab + {b^2}$
Now the given polynomial is ${(x + 4)^2}$.
We need to write its standard form. In order to write any polynomial equation in a standard form we have to rearrange it in the form of $a{x^2} + bx + c$.
${(x + 4)^2}$,
On using the formula,
$ \Rightarrow {(x + 4)^2} = {x^2} + 2(x)(4) + {4^2}$
That is ${x^2} + 8x + 16$
This is already in the form of $a{x^2} + bx + c$
Therefore, ${x^2} + 8x + 16$ is the standard form of the polynomial ${(x + 4)^2}$.