Questions: Multiply. (a-3)(4a+1) Simplify your answer.

Transcript text: Multiply. \[ (a-3)(4 a+1) \] Simplify your answer.

Solution

Solution Steps

Step 1: Expand the expression

To multiply \((a - 3)(4a + 1)\), use the distributive property (also known as the FOIL method for binomials). Multiply each term in the first parentheses by each term in the second parentheses:

\[ (a - 3)(4a + 1) = a \cdot 4a + a \cdot 1 - 3 \cdot 4a - 3 \cdot 1 \]

Step 2: Perform the multiplication

Calculate each multiplication separately:

\[ a \cdot 4a = 4a^2 \] \[ a \cdot 1 = a \] \[ -3 \cdot 4a = -12a \] \[ -3 \cdot 1 = -3 \]

Step 3: Combine like terms

Combine the terms \(a\) and \(-12a\):

\[ 4a^2 + a - 12a - 3 = 4a^2 - 11a - 3 \]

Final Answer

The simplified expression is:

\[ \boxed{4a^2 - 11a - 3} \]

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