Question

Factor each monomial completely.$\mathbf{-}\mathbf{13}\mathit{x}{\mathit{y}}^{\mathbf{3}}$

Short answer

The complete factorization of the monomial is$-1\times 13\times x\times y\times y\times y$.

Step-by-step solution

Step 1. State the concept for factorization of algebraic expressions.

1. The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
2. If x is a variable and m, n are positive integers, then$x^{m+n}=(x^m\times x^n)$

Step 2. State the methods to factorize.

Factoring an algebraic expression means writing the expression as a product of factors.

To verify whether the factors are correct or not, multiply them and check if the result is the original algebraic expression.

Algebraic expressions can be factorized using the common factor method, regrouping like terms together, and also by using algebraic identities.

Step 3. Expand the expression.

Solve the expression by expanding it.

$\begin{array}{c}-13x{y}^3=-1\times 13\times x{y}^3\\ =-1\times 13\times x\times y\times y\times y\end{array}$

Therefore, the result of the factorization is$-1\times 13\times x\times y\times y\times y$.