Chapter 8: Q50. (page 516)

Factor each polynomial.
$y^{2} - 81$ .

Short Answer

Expert verified

The factor of the polynomial is $(y - 9) (y + 9)$ .

Step by step solution

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

The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
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. Factorize the expression.

The expression can be factored as below:

$\begin{matrix} y^{2} - 81 = {(y)}^{2} - {(9)}^{2} \\ = (y - 9) (y + 9) \end{matrix}$

Therefore, the factor of the polynomial are $(y - 9) (y + 9)$ .

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Factor each polynomial.
$y^{2} - 81$ .

Short Answer

Step by step solution

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

Step 2. State the methods to factorize.

Step 3. Factorize the expression.

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Factor each polynomial.y2−81.

Short Answer

Step by step solution

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

Step 2. State the methods to factorize.

Step 3. Factorize the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Logic and Functions

Statistics

Discrete Mathematics

Theoretical and Mathematical Physics

Calculus

Study anywhere. Anytime. Across all devices.

Factor each polynomial.
$y^{2} - 81$ .