Question

What is the coefficient of the second term of the trinomial?

(4a+5)2=16a2+Ba+25

Enter your answer in the box.
B=

Answer 1

To find the coefficient \( B \) in the trinomial \( (4a + 5)^2 = 16a^2 + Ba + 25 \), we will expand \( (4a + 5)^2 \).

We can use the formula for the square of a binomial:

\[
(x + y)^2 = x^2 + 2xy + y^2
\]

In this case, \( x = 4a \) and \( y = 5 \). Plugging these values into the formula:

1. **Calculate \( x^2 \)**:
\[
(4a)^2 = 16a^2
\]

2. **Calculate \( 2xy \)**:
\[
2(4a)(5) = 40a
\]

3. **Calculate \( y^2 \)**:
\[
5^2 = 25
\]

Putting it all together, we have:

\[
(4a + 5)^2 = 16a^2 + 40a + 25
\]

Now, we can equate this to the expression given:

\[
16a^2 + Ba + 25
\]

From the expansion, we see that the coefficient of the term involving \( a \) is \( 40 \). Thus, we can conclude:

\[
B = 40
\]

The answer is:

\[
B = 40
\]