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Chapter 5: Problem 57

Find each product. In each case, neither factor is a monomial. $$(2 x+1)(x+4)$$

Short Answer

Expert verified
\(2x^2 + 9x + 4\)

Step by step solution

01

Apply the distributive property

Multiply each term in the first bracket \((2x + 1)\) by each term in the second bracket \((x + 4)\). There are four multiplication operations: \(2x \cdot x\), \(2x \cdot 4\), \(1 \cdot x\), \(1 \cdot 4\).
02

Carry out the multiplications

Perform the four multiplications: \(2x \cdot x = 2x^2\), \(2x \cdot 4 = 8x\), \(1 \cdot x = x\), \(1 \cdot 4 = 4\).
03

Sum up the results

Add up the results of the four multiplications to get the final answer: \(2x^2 + 8x + x + 4\).
04

Simplify

Combine the like terms \(8x\) and \(x\) to simplify the expression: \(2x^2 + 9x + 4\).

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