Find the following product.?

Question

(9x+9y)(8x-7y)

Answer 1

9x + 9y
* 8x - 7y
-----------------------------
-63xy-63y^2
72x^2 +72xy
------------------------------
72x^2 + 9xy - 63y^2

Answer 2

When you have two binomials (two terms connected by a plus or minus), you need to be sure that you use the Distributive property twice when you multiply. In other words, you need to multiply the first term in the first binomial (in this case 9x) by each term in the second binomial (the 8x and 7y).

To help you remember to do this double distribution, you may have learned the acronym FOIL, which reminds you of the four multiplications that need to be carried out.

F - first number of each parenthesis
O - outer numbers in the problem
I - inner numbers in the problem
L - last number in each parenthesis

So here are the four multiplications to be done:

F = 9x*8x = 72x^2
O = 9x*-7y = -63xy
I = 9y*8x = +72xy
L = 9y*-7y = -63y^2

Add all of these terms together to get your final answer. Remember that you can only combine like terms, those with the exact same variable. Notice that the answers to your "O" and "I" multiplications have the exact same variables, xy. This will always happen when you FOIL. Therefore, you want to add the coefficients (numbers in front of the xy's) to make one xy term before you are finished with your answers.

So your answer would be:

72x^2-63xy+72xy-63y^2

Combine the -63xy and +72xy to get +9xy as your middle term in your final trinomial:

72x^2+9xy-63y^2

Answer 3

(9x+9y)(8x-7y)

=72x^2 + 72xy - 63xy - 63y^2

=72x^2 - 63y^2 + 11xy

Answer 4

(9x+9y)(8x-7y)
9x(8x-7y) + 9y(8x-7y)
72x(x)-63xy + 72xy - 63y(y)
=72x(x)+9xy-63y(y)

Answer 5

8x^2+xy-7y^2

Answer 6

9(8x^2 - 7y^2 - xy)

Answer 7

72x^2+ 72xy - 63xy - 63y^2
= 72x^2 + 9xy - 63y^2

Answer 8

(9x+9y)(8x-7y)
=72x^2+72xy-63xy-63y^2
=72x^2+9xy-63y^2
=9(8x^2+xy-7y^2)