Answer:
(5a - [2b - 7c]) and (5a + [2b + 7c])
Explanation:
Factor 25a^2 - 4b^2 + 28bc - 49c^2.
Note that - 4b^2 + 28bc - 49c^2 involves the variables b and c, whereas 25a^2 has only one variable. Thus, try to rewrite - 4b^2 + 28bc - 49c^2 as the square of a binomial:
- 4b^2 + 28bc - 49c^2 = -(4b^2 - 28bc + 49c^2), or
-(2b - 7c)^2.
Thus, the original 25a^2 - 4b^2 + 28bc - 49c^2 looks like:
[5a]^2 - [2b - 7c]^2
Recall that a^2 - b^2 is a special product, the product of (a + b) and (a - b). Applying this pattern to the problem at hand, we conclude:
Thus, [5a]^2 - [2b - 7c]^2 has the factors (5a - [2b - 7c]) and (5a + [2b + 7c])