Find the product. Recall that $$ a^{2}=a \cdot a $$. $$ (5 p-2)^{2} $$ $$ (5 p-2)^{2}=\square $$ (Simplify your answer.)

Question

UpStudy AI · Accepted Answer

We start with the binomial square formula:
$$
(a-b)^2 = a^2 - 2ab + b^2.
$$

Here, let $$ a = 5p $$ and $$ b = 2 $$. Then we have:

1. Compute $$ a^2 $$:
$$
(5p)^2 = 25p^2.
$$

2. Compute $$ -2ab $$:
$$
-2 \cdot (5p) \cdot 2 = -20p.
$$

3. Compute $$ b^2 $$:
$$
2^2 = 4.
$$

Combine these:
$$
(5p-2)^2 = 25p^2 - 20p + 4.
$$

Thus, the simplified form is:
$$
(5p-2)^2 = 25p^2-20p+4.
$$
$$ (5p-2)^2 = 25p^2 - 20p + 4 $$

Find the product. Recall that \( a^{2}=a \cdot a \). \[ (5 p-2)^{2} \] \( (5 p-2)^{2}=\square \) (Simplify your answer.)