Problem 71 - College Algebra

Question

Find each product. $$(3 x y-1)(5 x y+2)$$

Step-by-Step Solution

Answer

The product of \((3 x y-1)(5 x y+2)\) is \[15x^{2}y^{2} + xy - 2\]

Step 1: Distribute First Term of First Binomial

Multiply the first term of the first binomial (3xy) by each term in the second binomial. \[(3xy)*(5xy) = 15x^{2}y^{2}\] and \[(3xy)*(2) = 6xy\]

Step 2: Distribute Second Term of First Binomial

Multiply the second term of the first binomial (-1) by each term in the second binomial. \[(-1)*(5xy) = -5xy\] and \[(-1)*(2) = -2\]

Step 3: Combine Like Terms

Combine the like terms that resulted from the multiplication. The term 6xy and -5xy are like terms, combine them to get xy. So, the final expression is: \[15x^{2}y^{2} + xy - 2\]