Problem 35 - College Algebra

Question

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

Step-by-Step Solution

Answer

So, the resulting product of \((5-7x)(5+7x)\) is \(25 - 49x^2\).

Step 1: Identify the terms in the binomials

The terms in each of the binomial expressions are identified. In the binomial \(5 - 7x\), 5 and -7x are the terms. In the binomial \(5 + 7x\), 5 and 7x are the terms.

Step 2: Apply the FOIL method

Multiply together pairs of terms using the FOIL method: (First, Outside, Inside, Last). First, multiply the first term of each binomial (5 * 5), then the outside terms (5 * 7x), the inside terms (-7x * 5), and finally, the last terms (-7x * 7x).

Step 3: Simplify the result

Combine like terms and simplify the resulting expression. This gives \(25 - 35x + 35x - 49x^2\). Combining the middle terms (-35x and 35x), which cancels each other out.