Question

How do you simplify ${(x + 8)^2}$ ?

Answer 1

Hint:${(x + 8)^2} = {x^2} + 16x + 64$. Solve the question by multiplying $(x + 8).(x + 8)$ and then simplify the equation to get the answer.

Complete step –by- step solution-
Method 1-Let $y = {(x + 8)^2}$
This can also be written as
$y = (x + 8).(x + 8)$
Because the power of $(x + 8)$ is 2 which implies the $(x + 8)$ is multiplied twice.
Therefore on solving the equation we get,
$y = x.x + x.8 + 8.x + 8.8$
After multiplication and combining the like terms together we get,
$y = {x^2} + 16x + 64$
Which is the required answer.
Method 2-$y = {(x + 8)^2}$
We can also solve this question by directly applying the formula and substituting the values in the formula from the given equation.
By applying ,
${(x + a)^2} = {x^2} + 2ax + {a^2}$
We get,
$y = {x^2} + 2.8.x + 8.8$
After performing the calculations,
$y = {x^2} + 16x + 64$
Note- In Method 1, FOIL rule is applied. It is the rule commonly used for factoring , meaning to start by multiplying the two first variables first, followed by the outer variables, then the middle variables and then the last variables.

Ex- when $(x + 8)$ is being multiplied by $(x + 8)$, we will first multiply ‘x’ by ‘x’
$x.x = {x^2}$
$x.8 = 8x$
$8.x - 8x$
$8.8 = 64$
The final answer will be like ${x^2} + 16x + 64$.