Problem 48 - College Algebra Essentials

Question

Find each product. $$\left(5 x^{2}-3\right)^{2}$$

Step-by-Step Solution

Answer

The result of squaring the binomial \((5x^2 - 3)^2\) is \(25x^4 - 30x^2 + 9\)

Step 1: Identify the terms

The first step is to identify the two terms in the binomial. In this case, the first term (a) is \(5x^2\), and the second term (b) is 3.

Step 2: Apply the formula

Second step is to apply the formula for squaring a binomial, which is \(a^2 - 2*a*b + b^2\). Substituting \(a = 5x^2\) and \(b = 3\) we get \((5x^2)^2 - 2*5x^2*3 + 3^2\).

Step 3: Simplify

Finally, simplify each part of the result. \((5x^2)^2\) is \(25x^4\), \(2*5x^2*3\) is \(30x^2\) and \(3^2\) is \(9\). Combined, these give the result \(25x^4 - 30x^2 + 9\).