Express 81p^2 - 49q^2 as products of two terms.
recall your differences of squares factoring: a^2-b^2 - (a+b)(a-b)
So, here you just have
(9p)^2 - (7q)^2
To express 81p^2 - 49q^2 as the product of two terms, we can use the difference of squares identity. The difference of squares identity states that a^2 - b^2 = (a + b)(a - b).
In this case, we have 81p^2 - 49q^2.
So, we can rewrite this expression as (9p)^2 - (7q)^2.
Using the difference of squares identity, this expression can be rewritten as (9p + 7q)(9p - 7q).
Therefore, 81p^2 - 49q^2 can be expressed as the product of two terms: (9p + 7q)(9p - 7q).
To express the expression 81p^2 - 49q^2 as products of two terms, we can use the difference of squares formula.
The difference of squares formula states that for any two terms a^2 - b^2, it can be factored as (a - b)(a + b).
In our case, we have 81p^2 - 49q^2. We can see that 81p^2 is a perfect square, as it can be written as (9p)^2, and similarly, 49q^2 is a perfect square, as it can be written as (7q)^2.
Using the difference of squares formula, we can express 81p^2 - 49q^2 as (9p - 7q)(9p + 7q), which are the two terms we are looking for.