Question

Determine whether 49x^6 − 81b^2 is a difference of two squares. If so, factor it. If not, explain why.

Answer 1

Answer:

Yes; $(7x^3+9b)(7x^3-9b)$

Step-by-step explanation:

A difference of squares is basically where you have two terms that can both be written in the form of $k^2$ and one is subtracting the other.

Here, the first term is $49x^6$ . We see that if we square root this, we will come out with the clean number: $7x^3$ (because $7x^3*7x^3=49x^6$).

The second term is $81b^2$ . Again, we see that if we square root this, we will get the clean result: $9b$ (because $9b*9b=81b^2$).

So, they are indeed both squares; thus, this is a difference of squares.

To factor it, we remember the formula for factoring $a^2-b^2$: $a^2-b^2=(a+b)(a-b)$

In this case, a = 7x^3 and b = 9b, so:

$49x^6-81b^2=(7x^3+9b)(7x^3-9b)$, and that's the answer.

Hope that helps!