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Question

Question: How do you simplify \({(x + 8)^2}\) ?...

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

Explanation

Solution

(x+8)2=x2+16x+64{(x + 8)^2} = {x^2} + 16x + 64. Solve the question by multiplying (x+8).(x+8)(x + 8).(x + 8) and then simplify the equation to get the answer.

Complete step –by- step solution-
Method 1-Let y=(x+8)2y = {(x + 8)^2}
This can also be written as
y=(x+8).(x+8)y = (x + 8).(x + 8)
Because the power of (x+8)(x + 8) is 2 which implies the (x+8)(x + 8) is multiplied twice.
Therefore on solving the equation we get,
y=x.x+x.8+8.x+8.8y = x.x + x.8 + 8.x + 8.8
After multiplication and combining the like terms together we get,
y=x2+16x+64y = {x^2} + 16x + 64
Which is the required answer.
Method 2-y=(x+8)2y = {(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{(x + a)^2} = {x^2} + 2ax + {a^2}
We get,
y=x2+2.8.x+8.8y = {x^2} + 2.8.x + 8.8
After performing the calculations,
y=x2+16x+64y = {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)(x + 8) is being multiplied by (x+8)(x + 8), we will first multiply ‘x’ by ‘x’
x.x=x2x.x = {x^2}
x.8=8xx.8 = 8x
8.x8x8.x - 8x
8.8=648.8 = 64
The final answer will be like x2+16x+64{x^2} + 16x + 64.