Questions: Difference of squares Factor completely. 5x^2 - 320=

Solution Steps

To factor the expression \(5x^2 - 320\) completely, we first look for a common factor in both terms. Then, we recognize the expression as a difference of squares, which can be factored using the identity \(a^2 - b^2 = (a - b)(a + b)\).

The given expression is \(5x^2 - 320\). First, we identify the common factor in both terms, which is 5. We can factor out 5 from the expression:

\[ 5x^2 - 320 = 5(x^2 - 64) \]

The expression inside the parentheses, \(x^2 - 64\), is a difference of squares. We can use the identity \(a^2 - b^2 = (a - b)(a + b)\) to factor it further. Here, \(a = x\) and \(b = 8\), since \(64 = 8^2\).

Applying the difference of squares formula, we have:

\[ x^2 - 64 = (x - 8)(x + 8) \]

Substituting back into the expression, we get:

\[ 5(x^2 - 64) = 5(x - 8)(x + 8) \]

Final Answer