Factor:
49^2+112r+64 =
49^2+112r+64 = ___
First take care of the exponents:
49^2=2401
Add like terms:
(2401+64)+112r
2401+64= 2465
2465 + 112r is your answer.
Since it said to factor, I suspected that there was a typo, I am pretty sure you meant
49t^2 + 12t + 64
= (7t + 8)(7t+8) or (7t+8)^2
Wouldn't you know it?
I complain about a typo, and then do one myself,
should have been
49t^2 + 112t + 64
= (7t + 8)(7t+8) or (7t+8)^2
To factor the expression 49^2 + 112r + 64, we can use the factoring technique called "perfect square trinomial."
A perfect square trinomial has the form (a + b)^2 = a^2 + 2ab + b^2.
In this case, the expression has the form of a perfect square trinomial: (7^2)^2 + 2(7^2)(r) + (8)^2.
Now, we can rewrite the expression using this form:
(7^2)^2 + 2(7^2)(r) + (8)^2
= (7^2 + 8)^2
Therefore, the factored form of the expression 49^2 + 112r + 64 is (7^2 + 8)^2.