Chapter 8.7, Problem 4P

a.

To determine

To calculate: factorize the equation by difference in square method.

Answer to Problem 4P

  $\left(5d+8\right)\left(5d-8\right)$

Explanation of Solution

Given:The expression is $25d^2-64$

Calculation:difference in square formula is givenby $a^2-b^2=\left(a+b\right)\left(a-b\right)$

  $25d^2-64=\left(5d+8\right)\left(5d-8\right)$

b.

To determine

To show: The characteristics that make the above calculation possible.

Explanation of Solution

Given:The binomial given $25d^2+64$

Reason:According to the difference between square theorem the quadratic equation may be written as a difference between the two squares such that it is factorize into two binomials where one is the sum and other is the difference of the roots of the squares. This theorem can be used

until there is a difference between the squares.

Here in the above equation 64 is the square of 8 while 25 is the square of 5same with the case of d but instead of difference there is the addition between the two squares.

Hence this characteristic makes the above solution not possible by difference between square theorem.