Express 81p^2 - 49q^2 as products of two terms.
a^2-b^2 = (a+b)(a-b)
To express the expression 81p^2 - 49q^2 as products of two terms, we need to identify a common factor between the two terms and then apply the difference of squares formula.
Step 1: Identify the common factor(s)
In this case, the common factor is the difference of squares between the two terms, which is 81p^2 - 49q^2.
Step 2: Apply the difference of squares formula
The difference of squares formula states that for any two terms, such as a^2 - b^2, it can be factored as (a + b)(a - b).
Applying the difference of squares formula to our expression, we have:
81p^2 - 49q^2 = (9p)^2 - (7q)^2
Step 3: Express as products of two terms
We can now express the expression as the product of two terms using the difference of squares formula:
81p^2 - 49q^2 = (9p + 7q)(9p - 7q)
Therefore, 81p^2 - 49q^2 can be expressed as the product of two terms: (9p + 7q)(9p - 7q).