Multiply using the rule for the product of the sum and difference of two terms. Assume any variable exponents represent whole numbers.
(x - y + 11)(x - y - 11)
Have you learned the rule that they are suggesting that you use? I strongly adise doing so. In this case, what you have is the sum and difference of the terms "x-y" and "11".
The general rule is
(a + b) (a - b) = a^2 - b^2
Please avoid name changes and the posting of long lists of questions with no work shown.
To multiply using the rule for the product of the sum and difference of two terms, follow these steps:
Step 1: Identify the terms within each parentheses.
In this case, the first set of parentheses is (x - y + 11) and the second set of parentheses is (x - y - 11).
Step 2: Apply the distributive property.
To expand the product, you need to distribute each term from the first set of parentheses to each term within the second set of parentheses.
(x - y + 11)(x - y - 11)
= x(x - y - 11) - y(x - y - 11) + 11(x - y - 11)
Step 3: Simplify each term.
Multiply each term within the parentheses by the corresponding term from the other set of parentheses:
= x(x) - x(y) - 11(x) - y(x) + y(y) + 11(y) + 11(x) - y(x) - 11(x) + 11(y) - 11(11)
Step 4: Combine like terms.
Group together like terms and simplify:
= x^2 - xy - 11x - xy + y^2 + 11y + 11x - xy - 11x + 11y - 121
Step 5: Further simplify.
Combine like terms again:
= x^2 - 2xy - 22x + y^2 + 22y - 121
Thus, the product of (x - y + 11)(x - y - 11) is x^2 - 2xy - 22x + y^2 + 22y - 121.