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Chapter 0: Problem 76

Find each product. $$(5 x+7 y-2)(5 x+7 y+2)$$

Short Answer

Expert verified
The result is \(25x^2 + 70xy - 14y + 49y^2 - 4\). In the expanded form, all the like terms are combined to simplify the equation.

Step by step solution

01

Distribute the First and Second Term

First, distribute the first term in the first binomial to each term in the second binomial. This gives you: \(5x(5x) + 5x(7y) + 5x(2)\) which simplifies to \(25x^2 + 35xy + 10x\)
02

Distribute the Second Term

Next, distribute the second term from the first binomial to each term in the second binomial. This results in: \(7y(5x) + 7y(7y) + 7y(2)\) which simplifies to \(35xy + 49y^2 + 14y\)
03

Distribute the Third Term

Finally, distribute the third term of the first binomial to the second binomial. This should result in: \(-2(5x) - 2(7y) - 2(2)\), which simplifies to \(-10x - 14y -4\).
04

Add the results from step 1, 2 and 3

Combine the results from steps one to three: \( (25x^2 + 35xy + 10x) + (35xy + 49y^2 + 14y) + (-10x - 14y -4)\), which simplifies to \(25x^2 + 70xy - 14y + 49y^2 - 4\)

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When performing the division $$\frac{7 x}{x+3}+\frac{(x+3)^{2}}{x-5}$$ I began by dividing the numerator and the denominator by the common factor, \(x+3\).

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