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Chapter 0: Problem 60

Find each product. $$(x+9 y)(6 x+7 y)$$

Short Answer

Expert verified
The product of the binomials \( (x+9y) \) and \( (6x+7y) \) is \(6x^2 + 61xy + 63y^2\).

Step by step solution

01

Apply the First rule

First, multiply the first terms of each binomial. That is, multiply \(x\) with \(6x\) which equals \(6x^2\).
02

Apply the Outer rule

Secondly, multiply the first term of the first binomial by the second term of the second binomial. In this case, multiply \(x\) and \(7y\) to get \(7xy\).
03

Apply the Inner rule

Thirdly, multiply the second term of the first binomial by the first term of the second binomial. This means multiplying \(9y\) and \(6x\) to obtain \(54xy\).
04

Apply the Last rule

Finally, multiply the second terms in each binomial. Multiply \(9y\) with \(7y\) to find \(63y^2\).
05

Add the results

Now add all the obtained terms from step 1 to step 4 to find the solution. \(6x^2 + 7xy + 54xy + 63y^2 = 6x^2 + 61xy + 63y^2\)

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