Question

Factor completely.

49t^6 - 4k^8

A.) (7t³ + 2k^4)(7t³ - 2k^4)
B.) (7t³ - 2k^4)(7t³ - 2k^4)
C.)(7t³ + 2k^4)(7t³ + 2k^4)

Answer 1

Answer:

A.) (7t³ + 2k^4)(7t³ - 2k^4)

Step-by-step explanation:

Factor the following:

49 t^6 - 4 k^8

49 t^6 - 4 k^8 = (7 t^3)^2 - (2 k^4)^2:

(7 t^3)^2 - (2 k^4)^2

Factor the difference of two squares. (7 t^3)^2 - (2 k^4)^2 = (7 t^3 - 2 k^4) (7 t^3 + 2 k^4):

Answer:  (7 t^3 - 2 k^4) (7 t^3 + 2 k^4)

Answer 2

Answer:

A.) (7t³ + 2k^4)(7t³ - 2k^4)

Step-by-step explanation:

This is what we call a conjugate binomial which is two binomials with similar terms but with one of those terms with different signs, this shows a result of the first term squared minus the second term squared.

The formula for conjugate binomials are:

(a+b)(a-b)= $a^{2}-b^{2}$

In this case the multiplication of

(7t³ + $2k^{8}$)(7t³ - $2k^{8}$ )= 49 $t^{6}$ + 14$k^{4}t^{3}$ - 14$k^{4}t^{3}$  - $4k^{8}$

After substracting the second and the third term you are left with:

$49t^{6} - 4k^{8}$