Question
Question: How do you simplify \({(x + 8)^2}\) ?...
How do you simplify (x+8)2 ?
Solution
(x+8)2=x2+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=x2+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=x2+2ax+a2
We get,
y=x2+2.8.x+8.8
After performing the calculations,
y=x2+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=x2
x.8=8x
8.x−8x
8.8=64
The final answer will be like x2+16x+64.