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Chapter 5: Problem 56

Find each product. In each case, neither factor is a monomial. $$(x+4)(x+6)$$

Short Answer

Expert verified
The product of the given binomials is \(x^2 + 10x + 24\).

Step by step solution

01

Apply the FOIL Method

Firstly, apply the FOIL method, which stands for First, Outer, Inner, Last (which means multiplying the first terms of both binomials, then the outer terms, the inner terms and finally, the last terms):\n First: \(x*x = x^2\), Outer: \(x*6 = 6x\), Inner: \(4*x = 4x\), Last: \(4*6 = 24\).
02

Combine Like Terms

Combine the Outer and Inner result because they are like terms. So, \(6x + 4x = 10x\).
03

Write the Final Result

Lastly, put all the results together to find the product of the given binomials: \(x^2 + 10x + 24\).

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