Chapter 8.7, Problem 47HP

To determine

To check which factorisation is correct.

Answer to Problem 47HP

Lorenzo is correct.

Explanation of Solution

Given:

Polynomial: $16x^4-25y^2$

  

Calculation:

Consider the given polynomial,

  $\Rightarrow 16x^4-25y^2$

Writing the terms in the form of $a^2-b^2,$

  $\Rightarrow {(4x^2)}^2-{(5y)}^2$

Factoring with the difference of squares,

  $\Rightarrow (4x^2-5y)(4x^2+5y)$

These steps are similar to that of Lorenzo’s answer.

Conclusion:

Therefore, Lorenzo is correct.