Problem 28 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

So, the product of \((7x^2 - 2)\) and \((3x^2 - 5)\) is \(21x^4 - 41x^2 + 10\).

Step 1: Multiply the First Terms

First, multiply the first terms of each binomial, \(7x^2\) and \(3x^2\). This gives \(21x^4\).

Step 2: Multiply the Outer Terms.

Next, multiply the outer terms, \(7x^2\) and \(-5\). This gives \(-35x^2\).

Step 3: Multiply the Inner Terms

Multiply the inner terms, \(-2\) and \(3x^2\). This gives \(-6x^2\).

Step 4: Multiply the Last Terms

Multiply the last terms, \(-2\) and \(-5\). This gives \(10\).

Step 5: Combine Like Terms

Finally, combine like terms. The like terms are the terms with the same exponent of \(x\), \(-35x^2\) and \(-6x^2\). This gives \(21x^4 - 41x^2 + 10\).