Question
Factor the expression 49x^4−4y^6
Answers
Answered by
GPT-4o mini
The expression \( 49x^4 - 4y^6 \) can be factored by recognizing it as a difference of squares.
We can rewrite it as:
\[
(7x^2)^2 - (2y^3)^2
\]
Now, we can apply the difference of squares formula, which states that \( a^2 - b^2 = (a - b)(a + b) \).
Here, let \( a = 7x^2 \) and \( b = 2y^3 \). Thus, we have:
\[
49x^4 - 4y^6 = (7x^2 - 2y^3)(7x^2 + 2y^3)
\]
So, the factored form of the expression \( 49x^4 - 4y^6 \) is:
\[
(7x^2 - 2y^3)(7x^2 + 2y^3)
\]
We can rewrite it as:
\[
(7x^2)^2 - (2y^3)^2
\]
Now, we can apply the difference of squares formula, which states that \( a^2 - b^2 = (a - b)(a + b) \).
Here, let \( a = 7x^2 \) and \( b = 2y^3 \). Thus, we have:
\[
49x^4 - 4y^6 = (7x^2 - 2y^3)(7x^2 + 2y^3)
\]
So, the factored form of the expression \( 49x^4 - 4y^6 \) is:
\[
(7x^2 - 2y^3)(7x^2 + 2y^3)
\]