(n+9)^2
n^2+81
(r-11)^2
r^2-22
(z+13)(z-13)
Z^2
(n+9) times (n+9)
FOIL n^2 +9n + 9n + 81 Do not forget the middle the O and the I
(r-11) times (r-11)
r^2 - 11r - 11r + 121
Can you guess why the third one is different? The positive and negative terms get rid of each other.
14
To understand how to get the answers, let's break down each expression step by step:
1. (n+9)^2
To simplify this expression, you can use the formula for the square of a binomial, which is (a+b)^2 = a^2 + 2ab + b^2. In this case, a is n and b is 9. So, (n+9)^2 becomes:
n^2 + 2*n*9 + 9^2
Simplifying further:
n^2 + 18n + 81
2. n^2 + 81
This expression is already in its simplest form. There are no common factors or square terms to combine.
3. (r-11)^2
Using the same formula for the square of a binomial, with a = r and b = -11:
(r-11)^2 becomes:
r^2 + 2*r*(-11) + (-11)^2
Simplifying further:
r^2 - 22r + 121
4. r^2 - 22
This expression seems to be incomplete as it is missing a term with r. Please double-check if there is any missing information.
5. (z+13)(z-13)
This expression is in the form of a difference of squares, which can be simplified using the formula (a+b)(a-b) = a^2 - b^2. In this case, a is z and b is 13. So, (z+13)(z-13) becomes:
z^2 - 13^2
Simplifying further:
z^2 - 169
Therefore, the final simplified expressions are:
1. (n+9)^2 = n^2 + 18n + 81
2. n^2 + 81 (already simplified)
3. (r-11)^2 = r^2 - 22r + 121
4. r^2 - 22 (incomplete expression, needs further information)
5. (z+13)(z-13) = z^2 - 169