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Problem 10

# $$(3 x+1)^{2}$$

Expert verified
The expanded form of the given expression $$(3x+1)^2$$ is $$9x^2 + 6x + 1$$.
See the step by step solution

## Step 1: Identify the values of a and b

In the expression $$(3x + 1)^2$$, we can see that $$a = 3x$$ and $$b = 1$$.

## Step 2: Apply the binomial square formula

Use the formula $$(a+b)^2 = a^2 + 2ab + b^2$$, and substitute the values of $$a$$ and $$b$$ that we identified in Step 1. $$(3x+1)^2 = (3x)^2 + 2(3x)(1) + (1)^2$$

## Step 3: Simplify the terms

Simplify each term in the expanded expression: $$(3x)^2 = 9x^2$$ $$2(3x)(1) = 6x$$ $$(1)^2 = 1$$

## Step 4: Combine the simplified terms

Combine the simplified terms from Step 3 to obtain the final expanded expression: $$(3x+1)^2 = 9x^2 + 6x + 1$$ So, the expanded form of the given expression is $$9x^2 + 6x + 1$$.

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