Problem 48 - College Algebra

Question

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

Step-by-Step Solution

Answer

The product of \((5x^2 - 3)^2\) is \(25x^4 - 30x^2 + 9\).

Step 1: Identify 'a' and 'b'

In the expression \( (5x^2 - 3)^2 \), 'a' is \(5x^2\) and 'b' is \(3\). We will substitute these values into the formula \((a - b)^2 = a^2 - 2ab + b^2 \)

Step 2: Substitute 'a' and 'b' in the formula

On substituting \(a = 5x^2\) and \(b = 3\) in the formula we get \((5x^2 - 3)^2 = (5x^2)^2 - 2*5x^2*3 + 3^2 \)

Step 3: Solve the resulting expression

Now solve the expression. So, \( (5x^2)^2 = 25x^4 \), \( 2*5x^2*3 = 30x^2 \), and \( 3^2 = 9 \). Thus, \((5x^2 - 3)^2 = 25x^4 - 30x^2 + 9 \)