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Chapter 0: Problem 78

Find each product. $$[8 y+(7-3 x)][8 y-(7-3 x)]$$

Short Answer

Expert verified
The product is \(9x^2 - 42x + 64y^2 + 49\)

Step by step solution

01

Identify terms in the formula

The terms of the exercise fit into the formula for difference of squares. Recognise \(8y\) as \(a\), and \(7 - 3x\) as \(b\). The exercise is then re-written as \(a^2 - b^2\)
02

Apply the formula for the difference of squares

The formula for the difference of squares is \(a^2 - b^2 = (a + b)(a - b)\). Thus, we have \(( 8y + (7 - 3x) ) ( 8y - (7 - 3x) )\)
03

Calculate the product

To find the result, calculate the square of each term (i.e. \(a^2 - b^2\), which is \((8y)^2 - (7 - 3x)^2\), and after calculation this equates to \(64y^2 - (49 - 42x + 9x^2)\), and simplifying further results in \(64y^2 - 49 + 42x - 9x^2\), therefore the result is \(9x^2 - 42x + 64y^2 + 49\)

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