Question

36f^2+84f+49

Idk what to do?? Thanks for the help!

Answer 1

Since the first and last terms are perfect squares, become suspicious and

test if it is perfect square.
sure enough, I get
(6f + 7)^2

Answer 2

36 and 49 are both perfect squares which makes me suspicious

(6 f +/- 7) (6 f +/- 7) ???
oh my 6*7 = 42 and twice that is 84, we have it made
(6 f+7)(6 f+7)
You did not say what is on the right. If it is 0 then
f = -7/6, -7/6 and that is the vertex

Answer 3

thanks!! can you tell me how you got rid of the 84f? Since 36=6f and then the +7 represent 49.

Answer 4

(6 f+7)(6 f+7)

now let's do that multiplication the long way
6 f (6 f + 7) + 7 (6 f + 7) = 6f *6f + 6f*7 + 6f*7 + 7*7
= 36 f^2 + 42 f + 42 f + 49
= 36 f^2 + 84 f+ 49

see that 42 f + 42 f = 84 f?

Answer 5

[AI-generated answer — Explain Bot]

To simplify the expression 36f^2 + 84f + 49, you can use the concept of factoring.

Step 1: Look for common factors, if any. In this expression, there are no common factors among the coefficients 36, 84, and 49.

Step 2: Check if it can be factored using a pattern. In this case, it cannot be factored using any common patterns.

Step 3: Factor the quadratic expression using the quadratic formula or by completing the square. However, this expression is not a quadratic expression in the standard form (ax^2 + bx + c), so these methods cannot be used.

Step 4: Since the expression cannot be further simplified through factoring, the expression 36f^2 + 84f + 49 is already in its simplest form.

Therefore, the simplified form of the expression 36f^2 + 84f + 49 is 36f^2 + 84f + 49 itself.