4.7k views
5 votes
Factor the following expression. 49x^(2)-25 Select one: 7(x^(2)+5) (7x+5)(7x-5) (7x-5)^(2) (7x+5)^(2)

1 Answer

3 votes

Final answer:

The expression 49x^(2)-25 is factored as (7x + 5)(7x - 5), which is the result of applying the difference of squares formula a^2 - b^2 = (a + b)(a - b).

Step-by-step explanation:

To factor the expression 49x^(2)-25, we recognize it as a difference of squares. Since both 49 and 25 are perfect squares, we can rewrite this expression as (7x)^2 - 5^2. The difference of squares can be factored using the formula a^2 - b^2 = (a + b)(a - b).

Therefore, the factored form of the expression is:

(7x + 5)(7x - 5)

Remember that when you raise each expression inside parentheses to a power, the power affects everything inside the parentheses including the number. This concept is similar to when we raise whole expressions to an integer power. For instance, (2x)^2 = 2^2 * x^2. Thus, it's clear we apply the exponents to both the coefficient and the variable.

User Edem
by
7.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories