solve by factoring
a^2 -121 = 0
(a-11)(a-11)
is this correct?
all you did was to factor it, but it said 'solve'
Besides you did not see the difference of squares to get
(a-11)(a+11) = 0
then
a = 11 or a = -11
To check if the factoring is correct, expand the factored form to see if it simplifies back to the original equation.
Let's expand (a - 11)(a - 11):
(a - 11)(a - 11) = a(a) + a(-11) + (-11)(a) + (-11)(-11)
= a^2 - 11a - 11a + 121
= a^2 - 22a + 121
As you can see, the expanded form is not equal to the original equation a^2 - 121. Therefore, (a - 11)(a - 11) is not the correct factored form of the equation.
To correctly factor a^2 - 121 = 0, we need to use a difference of squares formula:
a^2 - b^2 = (a + b)(a - b)
In this case, a^2 - 121 can be written as a^2 - 11^2, where b = 11.
So the correct factored form of a^2 - 121 = 0 is:
(a - 11)(a + 11)