Question

Multiply (4x + 7)2.

16x2 + 49
16x2 + 28x + 49
16x2 + 56x + 49
8x2 + 14

Answer 1

To multiply \( (4x + 7)^2 \), we can use the formula for squaring a binomial, which is \( (a + b)^2 = a^2 + 2ab + b^2 \).

Here, \( a = 4x \) and \( b = 7 \).

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

2. Calculate \( 2ab \):
\[
2 \cdot (4x) \cdot 7 = 56x
\]

3. Calculate \( b^2 \):
\[
7^2 = 49
\]

Now, combine these results:
\[
(4x + 7)^2 = 16x^2 + 56x + 49
\]

Thus, the final answer is:
\[
\boxed{16x^2 + 56x + 49}
\]