no it doesn't
(a - 7)^2 + (a - 14)^2 = 2a^2 - 42a + 245
Where's your work?
(a - 7)^2 + (a - 14)^2 = a^2
First, we rewrite equation
(a - 7)(a - 7) + (a - 14)(a - 14) = a^2
Next use First, Outer, Inner, Last (FOIL)
a * a + (-7)a + (-7)a + (-7)(-7) + a * a + (-14)a + (-14)a + (-14)(-14) = a^2
Then simplify
a^2 - 14a + 49 + a^2 - 28a + 196 = a^2
Combine like terms
2a^2 - 42a + 245 = a^2
Subract a^2 from each side:
a^2 - 42a + 245 = 0
Now we Factor trinomial
(a - 35)(a - 7) = 0
What happens here is, using FOIL again, we start with
(a - b)(a - c) = 0
Then we find what b and c are, their sum must be 42 and their product must be 245.
35 * 7 = 245
35 + 7 = 42
(35 - 35)(35 - 7) = 0, (7 - 35)(7 - 7) = 0 also.
So we have:
(35 - 7)^2 + (35 - 14)^2 = 35^2
28^2 + 21^2 = 35^2
784 + 441 = 1225
Or:
(7 - 7)^2 + (7 -14)^2 = 7^2
0 + -7^2 = 7^2
49 = 49