Multiply.

Question

left parenthesis 5 w plus 3 t right parenthesis left parenthesis 5 w minus 3 t right parenthesis
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Part 1
left parenthesis 5 w plus 3 t right parenthesis left parenthesis 5 w minus 3 t right parenthesisequals
  
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​(Simplify your​ answer.)

Answer 1

To multiply the expressions \( (5w + 3t)(5w - 3t) \), we can use the difference of squares formula, which states that:

\[ (a + b)(a - b) = a^2 - b^2 \]

In this case, let:

• \( a = 5w \)
• \( b = 3t \)

Now we can apply the formula:

\[ (5w + 3t)(5w - 3t) = (5w)^2 - (3t)^2 \]

Now, calculate each squared term:

\[ (5w)^2 = 25w^2 \] \[ (3t)^2 = 9t^2 \]

Putting it all together:

\[ (5w + 3t)(5w - 3t) = 25w^2 - 9t^2 \]

Thus, the simplified result is:

\[ \boxed{25w^2 - 9t^2} \]