Question

express the power (3a-1)^2 as a product of 2 bionomials and multiply them
(3a-1)^2=___=___

Answer 1

To express \((3a - 1)^2\) as a product of two binomials, we can use the formula for the square of a binomial:

\[
(x - y)^2 = (x - y)(x - y)
\]

For \((3a - 1)^2\), you can rewrite it as:

\[
(3a - 1)(3a - 1)
\]

Now, let's multiply the two binomials:

\[
(3a - 1)(3a - 1) = 3a \cdot 3a - 3a \cdot 1 - 1 \cdot 3a + 1 \cdot 1
\]

Calculating this step by step:

1. \(3a \cdot 3a = 9a^2\)
2. \(- 3a \cdot 1 = -3a\)
3. \(- 1 \cdot 3a = -3a\)
4. \(1 \cdot 1 = 1\)

Now combine like terms:

\[
9a^2 - 3a - 3a + 1 = 9a^2 - 6a + 1
\]

So, the expressions can be summarized as follows:

\[
(3a - 1)^2 = (3a - 1)(3a - 1) = 9a^2 - 6a + 1
\]

Thus:

\[
(3a - 1)^2 = (3a - 1)(3a - 1) = 9a^2 - 6a + 1
\]