Question

write 16-(3-4b)^2 as a product

Answer 1

To write \( 16 - (3 - 4b)^2 \) as a product, we can recognize that it has the form of a difference of squares. The expression can be rearranged as follows:

\[
16 - (3 - 4b)^2 = 4^2 - (3 - 4b)^2
\]

Now, we can apply the difference of squares formula, which states that \( a^2 - b^2 = (a - b)(a + b) \). Here, \( a = 4 \) and \( b = (3 - 4b) \).

Applying the difference of squares:

\[
4^2 - (3 - 4b)^2 = (4 - (3 - 4b))(4 + (3 - 4b))
\]

Now, we simplify both brackets:

1. For \( 4 - (3 - 4b) \):
\[
4 - 3 + 4b = 1 + 4b
\]

2. For \( 4 + (3 - 4b) \):
\[
4 + 3 - 4b = 7 - 4b
\]

Putting it all together, we have:

\[
16 - (3 - 4b)^2 = (1 + 4b)(7 - 4b)
\]

Thus, the expression \( 16 - (3 - 4b)^2 \) as a product is:

\[
(1 + 4b)(7 - 4b)
\]