Problem 142 - Algebra and Trigonometry

Question

Exercises \(142-144\) will help you prepare for the material covered in the next section. $$\text { Multiply: }\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)$$

Step-by-Step Solution

Answer

Hence, the product of \((2x^{3}y^{2})(5x^{4}y^{7})\) is \(10x^7y^9\).

Step 1: Multiply the coefficients

First, multiply the coefficients of the two terms. The coefficients are 2 and 5 and the product is 10.

Step 2: Multiply the powers of x

Next, multiply the powers of x. When multiplying variables, the powers of the variables add up. Here, \(x^3\) and \(x^4\) will result in \(x^{3+4}\) or \(x^7\).

Step 3: Multiply the powers of y

Finally, multiply the powers of y. The powers of \(y^2\) and \(y^7\) upon multiplication will add up to \(y^{2+7}\) or \(y^9\).