Question

. Complete the square for x 2 − 16x + __ .
Then write the resulting expression as a binomial squared.
a. −64; (x + 8) 2

b. −64; (x − 8)

c. 64; (x − 8) 22

d. 64; (x + 8) 2

Answer 1

Correct Answer: Option C

The given expression is:

$x^{2} -16x$

The formula for complete square is:

$(a-b)^{2} = a^{2} -2ab+ b^{2}$

The given expression can be re-written as:

$x^{2} -2(x)(8)$

So, we have the square of first term which x and twice the product of first and second term x and 8. What is missing is the square of second term. Second term is 8. So square of 8 which equals 64 is missing.

Therefore, complete square will be:

$x^{2} -2(x)(8)+ 8^{2} \\ \\ =(x-8)^{2}$