Explanation

In Quantity A, the term xy2z on the outside of the parentheses must be multiplied by each of the three terms inside the parentheses. Then simplify the expression as much as possible.

Taking one term at a time, the first is \(xy^2z \times x^2z = x^3y^2z^2\), because there are three factors of x, two factors of y, and two factors of z. Similarly, the second term is \(xy^2z \times yz^2 = xy^3z^3\) and the third is \(xy^2z \times (-xy^2) = -x^2y^4z\).

Adding these three terms together gives the distributed form of Quantity A: \(x^3y^2z^2 + xy^3z^3 - x^2y^4z\).

This is identical to Quantity B, so the two quantities are equal.