Problem 27 - College Algebra

Question

Find each product. $$\left(5 x^{2}-4\right)\left(3 x^{2}-7\right)$$

Step-by-Step Solution

Answer

The product of \((5x^2 - 4) * (3x^2 - 7)\) is \(15x^4 - 47x^2 + 28\).

Step 1: Multiply the First terms

Multiply the first terms of each binomial. That is \(5x^2 * 3x^2 = 15x^4\)

Step 2: Multiply the Outer terms

Multiply the outer terms of the two binomials. That is \(5x^2 * -7 = -35x^2\)

Step 3: Multiply the Inner terms

Multiply the inner terms of the two binomials. That is \(-4 * 3x^2 = -12x^2\)

Step 4: Multiply the Last terms

Multiply the last terms of each binomial. That is \(-4 * -7 = 28\)

Step 5: Combine Like Terms

Combine the like-terms from the results of the previous steps. The final answer will be: \(15x^4 - 35x^2 - 12x^2 + 28 = 15x^4 - 47x^2 + 28\)