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91Ó°ÊÓ

Find each product. $$(3 x+7-5 y)(3 x+7+5 y)$$

Short Answer

Expert verified
The product \((3x+7-5y)(3x+7+5y)\) simplifies to \(9x^2 + 42x - 25y^2 +49\).

Step by step solution

01

- Identify a and b

Identify \(a\) and \(b\) in the given trinomials. Here, \(a=3x+7\) and \(b=5y\).
02

- Apply Formula

Use the formula \(a^2 - b^2 = (a+b)(a-b)\) to rewrite the expression as \(a^2 - b^2\). So, \((3x+7+5y)(3x+7-5y)\) becomes \((3x+7)^2 - (5y)^2\).
03

- Simplify

Now, simplify the expression using the rules of algebra to perform the square operations. That results in \(9x^2 + 42x + 49 - 25y^2\).

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