Question

Find the product. $$(3 s+4 t)(3 s-4 t)$$

Short answer

The product of the two binomials \(3s + 4t\) and \(3s - 4t\) is \(9s^2 - 16t^2\).

Step-by-step solution

Apply the FOIL method

The goal is to multiply each term in the first binomial by each term in the second binomial. Start by multiplying the first terms in each binomial \((3s)(3s) = 9s^2\).

Multiply the Outer terms

Multiply the outer terms in each binomial \((3s)(-4t) = -12st\).

Multiply the Inner terms

Now, multiply the inside terms in each binomial \((4t)(3s) = 12st\).

Multiply the Last terms

Last, multiply the last terms from each binomial \((4t)(-4t) = -16t^2\).

Combine Like Terms

Now add all results together and combine like terms. Adding -12st and +12st makes the term disappear as they cancel each other. The final result is \(9s^2 - 16t^2\)