Question 10
Find the difference of $49 v^{6}$ and $25 b^{4}$.
Then completely factor the resulting binomial.
Answer =
Show your work here:
Answer
Final Answer: The difference of $49 v^{6}$ and $25 b^{4}$ is $-25 b^{4} + 49 v^{6}$. When factored, the resulting binomial is $(-5 b^{2} + 7 v^{3})(5 b^{2} + 7 v^{3})$. Therefore, the answer is \(\boxed{(-5 b^{2} + 7 v^{3})(5 b^{2} + 7 v^{3})}\).
Step 1 ：The problem is asking for the difference between two terms, $49 v^{6}$ and $25 b^{4}$, and then to factor the resulting binomial.
Step 2 ：First, we find the difference between the two terms by subtracting the second term from the first, which gives us $-25 b^{4} + 49 v^{6}$.
Step 3 ：Next, we factor the resulting binomial. Factoring is the process of breaking down a mathematical expression into its simplest components.
Step 4 ：The factored form of the binomial is $(-5 b^{2} + 7 v^{3})(5 b^{2} + 7 v^{3})$.
Step 5 ：Final Answer: The difference of $49 v^{6}$ and $25 b^{4}$ is $-25 b^{4} + 49 v^{6}$. When factored, the resulting binomial is $(-5 b^{2} + 7 v^{3})(5 b^{2} + 7 v^{3})$. Therefore, the answer is \(\boxed{(-5 b^{2} + 7 v^{3})(5 b^{2} + 7 v^{3})}\).
