Question

1. factor the binomial ( x^6 - 225 ) using the difference of squares formula.

( (x^2 + 15)(x^2 - 15) )
( (x^3 + 15)(x^3 - 15) )
( (x^6 + 15)(x^6 - 15) )
( (x^3 + 16)(x^3 - 16) )

Explanation:

The difference of squares formula is \(a^{2}-b^{2}=(a + b)(a - b)\). For the binomial \(x^{6}-225\), we can rewrite \(x^{6}\) as \((x^{3})^{2}\) and \(225\) as \(15^{2}\). So, applying the difference of squares formula, we get \((x^{3})^{2}-15^{2}=(x^{3}+15)(x^{3}-15)\).

Answer:

B. \((x^{3}+15)(x^{3}-15)\)