Chapter 8.2, Problem 15PPS

To determine

To factor: The given polynomial.

Answer to Problem 15PPS

The factorized form of the polynomialis $8\left(2t-5y\right)$ .

Explanation of Solution

Given information:

The polynomialis $16t-40y$ .

Formula used:

The distribution laws stated as multiply a number by groups of numbers having subtraction or addition operation between them same as multiplication done separately. That is,

  $\begin{array}{l}ab-ac-ad=a\left(b-c-d\right)\\ ab+ac+ad=a\left(b+c+d\right)\end{array}$

Concept used:

Factorized form of a polynomial is the product form of some binomial or trinomials or product of a constant and a polynomial.

Calculation:

Consider the given polynomial.

  $16t-40y$

Recall that the distribution laws stated as multiply a number by groups of numbers having subtraction operation between them same as multiplication done separately. That is,

  $ab-ac=a\left(b-c\right)$

Apply it and take $8$ common from each term of the polynomial.

  $\begin{array}{c}16t-40y=8\times 2t-8\times 5y\\ =8\left(2t-5y\right)\end{array}$

Thus, the factorized form is $16t-40y=8\left(2t-5y\right)$ .