Problem 69 - College Algebra

Question

Find each product. $$(x-3 y)(2 x+7 y)$$

Step-by-Step Solution

Answer

The product of the binomials \((x-3 y)(2 x+7 y)\) equals \(2x^2 + xy - 21y^2\).

Step 1: Distributing the first term

Take the first term from the first bracket, \(x\), and multiply it with both terms in the second bracket. That gives: \(x \times 2x = 2x^2\) and \(x \times 7y = 7xy\). The expression becomes: \(2x^2+7xy\).

Step 2: Distributing the second term

Take the second term of the first bracket, \(-3y\), and multiply it by both terms in the second bracket to get: \(-3y \times 2x = -6xy\) and \(-3y \times 7y = -21y^2\). Now our expression becomes: \(2x^2+7xy-6xy-21y^2\).

Step 3: Combining like terms

Combine the like terms which are \(7xy\) and \(-6xy\). Now we will have a final expression : \(2x^2 + (7xy - 6xy) - 21y^2\).

Step 4: Simplifying the expression

Simplify the expression in the bracket: \(2x^2 + xy - 21y^2\). This is our final result.