Problem 28 - College Algebra

Question

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

Step-by-Step Solution

Answer

The product of \((7 x^{2}-2)\) and \((3 x^{2}-5)\) is \(21x^4 - 41x^2 + 10\)

Step 1: Apply Distributive Law part 1

Multiply the first term in the first expression, \(7x^2\), with each term in the second expression: \(7x^2 * 3x^2 = 21x^4\), \(7x^2 * -5 = -35x^2\)

Step 2: Apply Distributive Law part 2

Next, multiply the second term in the first expression, -2, with each term in the second expression: \(-2 * 3x^2 = -6x^2\), \(-2 * -5 = 10\)

Step 3: Combine Like Terms

Now, combine like terms: \(21x^4 - 35x^2 - 6x^2 + 10\). This simplifies to \(21x^4 - 41x^2 + 10\)