Question

Find the product. $$(2 x-3)(5 x-9)$$

Short answer

The product of the two binomials (2x-3) and (5x-9) is \(10x^2 - 33x + 27\)

Step-by-step solution

Multiply the First terms

First, multiply the first term of the first binomial with the first term of the second binomial. This gives: \(2x * 5x = 10x^2\)

Multiply the Outer terms

Then, multiply the first term of the first binomial by the second term of the second binomial (outer terms). This gives: \(2x * -9 = -18x\)

Multiply the Inner terms

Next, multiply the second term of the first binomial by the first term of the second binomial (inner terms). This gives: \(-3 * 5x = -15x\)

Multiply the Last terms

Lastly, multiply the second term of the first binomial by the second term of the second binomial. This gives: \(-3 * -9 = 27\)

Combine the results

Combine the results to get final expression: \(10x^2 - 18x - 15x + 27 = 10x^2 - 33x + 27\).