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Chapter 5: Problem 40

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

Short Answer

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

Step by step solution

01

Multiply the first terms

Multiply the first terms from each binomial: \(x * 6x\), which is equal to \(6x^2\).
02

Multiply the outer terms

Multiply the outer terms: \(x * 7y\), which equals \(7xy\).
03

Multiply the inner terms

Next, the inner terms are multiplied: \(9y * 6x\), which equals \(54xy\).
04

Multiply the last terms

Then, the last terms are multiplied: \(9y * 7y\), giving \(63y^2\).
05

Add all the products

Finally, add all those products together, giving: \(6x^2 + 7xy + 54xy + 63y^2\). This is almost the final answer.
06

Simplify

Add together any similar terms: \(6x^2 + 61xy + 63y^2\).

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