find the product.(7x^2-y)(7x^2+y)

(7x^2 – y) (7x^2 + y)

49x^4 + 7x^2 y -7x^2 y – y^2
49x^4 –y^2

To find the product of (7x^2 - y) and (7x^2 + y), we will use the FOIL method.

FOIL stands for First, Outer, Inner, Last, and it is a helpful method for multiplying two binomials.

First, multiply the terms in the first positions of each binomial:
(7x^2) * (7x^2) = 49x^4

Outer, multiply the terms on the outside of each binomial:
(7x^2) * (y) = 7x^2y

Inner, multiply the terms on the inside of each binomial:
(-y) * (7x^2) = -7x^2y

Last, multiply the terms in the last positions of each binomial:
(-y) * (y) = -y^2

Now we have our four products: 49x^4, 7x^2y, -7x^2y, and -y^2.

Combine these products:
49x^4 + 7x^2y - 7x^2y - y^2

The two middle terms, 7x^2y and -7x^2y, cancel each other out. So the final product is:
49x^4 - y^2