Question

Use the formula a^2-b^2=(a+b)(a-b) to factor completely what are the factors of 36x^8-49

Answer 1

Can you guys please help me with my questions

Answer 2

Answer:

The factors  are:   $(6\,x^4+7)(6\,x^4-7)$

Step-by-step explanation:

Start by trying to find how to write each term as a perfect square, that way you know what your "a" and "b" values should be.

Notice that:   $36\,x^8 = 6^2\,(x^4)^2 = (6\,x^4)^2$

So, it is the perfect square of the quantity $6\,x^4$ (this is the "a" value that you need to use in your formula)

49 can also be written as a perfect square of 7:   $49=7^2$

Therefore, 7 is the "b" value for the formula you are asked to use.

Now we can write:

$36\,x^8-49=(6\,x^4)^2-7^2$

Then the formula goes as:

$a^2-b^2=(a+b)(a-b)\\(6\,x^4)^2-7^2=(6\,x^4+7)(6\,x^4-7)$

Then the factors we are looking for are: $(6\,x^4+7)(6\,x^4-7)$