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