Problem 27 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

The product of the given polynomials is \(15x^4 - 47x^2 + 28\).

Step 1: Multiply the First Terms

Multiply the first term of the first binomial \(5x^2\) by the first term of the second binomial \(3x^2\). This gives us \(15x^4\).

Step 2: Multiply the Outer Terms

Multiply the first term of the first binomial \(5x^2\) by the second term of the second binomial \(-7\). This gives us \(-35x^2\).

Step 3: Multiply the Inner Terms

Multiply the second term of the first binomial \(-4\) by the first term of the second binomial \(3x^2\). This gives us \(-12x^2\).

Step 4: Multiply the Last Terms

Multiply the second term of the first binomial \(-4\) by the second term of the second binomial \(-7\). This gives us \(28\).

Step 5: Combine Like Terms

Add \(-35x^2\) and \(-12x^2\) to get \(-47x^2\), because they are the like terms.

Step 6: Write the Final Result

Write the result by combining all the terms from step 1 to step 5, you'll obtain \(15x^4 - 47x^2 + 28\).