Chapter 8, Problem 40SGR

To determine

To use distributive property to factor the given polynomial.

Answer to Problem 40SGR

  $2y(4x-8x^3+5)$

Explanation of Solution

Given:

Polynomial: $8xy-16x^{3}y+10y$

Concept used:

Distributive property: $a(b+c)=a\cdot b+a\cdot c$

Calculation:

Consider the polynomial $8xy-16x^{3}y+10y$ ,

Applying the distributive property,

Finding out the common terms in each term of the expression,

Here, 2y is the common term.

  $\begin{array}{l}\Rightarrow 8xy-16x^{3}y+10y\\ \Rightarrow 2y(4x-8x^3+5)\end{array}$

Conclusion:

Therefore, the factors of the given polynomial are $2y(4x-8x^3+5).$