Question

question
factor completely.
$49x^2y^6 - 25$
answer attempt 1 out of 2

Explanation:

Step1: Identify the form of the expression

The given expression is \(49x^{2}y^{6}-25\), which is a difference of two squares. The formula for factoring a difference of squares is \(a^{2}-b^{2}=(a + b)(a - b)\).

Step2: Determine \(a\) and \(b\)

For \(49x^{2}y^{6}\), we can write it as \((7xy^{3})^{2}\) since \((7xy^{3})^{2}=7^{2}\times(x)^{2}\times(y^{3})^{2}=49x^{2}y^{6}\). For \(25\), we can write it as \(5^{2}\) since \(5^{2} = 25\). So, \(a = 7xy^{3}\) and \(b=5\).

Step3: Apply the difference of squares formula

Using the formula \(a^{2}-b^{2}=(a + b)(a - b)\) with \(a = 7xy^{3}\) and \(b = 5\), we get:
\(49x^{2}y^{6}-25=(7xy^{3}+5)(7xy^{3}-5)\)

Answer:

\((7xy^{3} + 5)(7xy^{3}-5)\)