Chapter 8, Problem 69SGR

To determine

To factorize the given polynomial

Answer to Problem 69SGR

  $-(y-9)(y+9)$

Explanation of Solution

Given:

Polynomial: $64-25x^2$

Formula used:

  $a^2-b^2=(a-b)(a+b)$

Calculation:

Consider the given polynomial,

  $\begin{array}{l}\Rightarrow 64-25x^2\\ \Rightarrow -(-64+25x^2)\\ \Rightarrow -(25x^2-64)\\ $ \Rightarrow -({(5x)}^2-8^2)$\Rightarrow -(y-8)(y+8)[\because a^2-b^2=(a-b)(a+b)]\end{array}$

Conclusion:

Therefore, the factors of the polynomial are $-(y-9)(y+9).$