Factor each trinomial completely. If the trinomial can not be factored state it is prime. The expression shown in the image is:\[ x^2 - 5xy + 6y^2 \]This is a quadratic expression with two variables, $x$ and $y$. It consists of three terms: - $x^2$ represents the square of $x$,- $-5xy$ represents the product of $-5$, $x$, and $y$,- $6y^2$ represents the square of $y$ multiplied by 6.This type of expression is commonly evaluated or factored in algebra to simplify equations or solve for variable values.

Answered: x2-5x1 t6

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Factor each trinomial completely. If the trinomial can not be factored state it is prime.

The expression shown in the image is:

\[ x^2 - 5xy + 6y^2 \]

This is a quadratic expression with two variables, $x$ and $y$. It consists of three terms:
- $x^2$ represents the square of $x$,
- $-5xy$ represents the product of $-5$, $x$, and $y$,
- $6y^2$ represents the square of $y$ multiplied by 6.

This type of expression is commonly evaluated or factored in algebra to simplify equations or solve for variable values.

Expert Solution

Step 1

Given trinomial is $x^{2} - 5 x y + 6 y^{2}$ .

We will factorize the given trinomial.

$\begin{array}{rcl} x^{2} - 5 x y + 6 y^{2} & = & x^{2} - 2 x y - 3 x y + 6 y^{2} \\ = & x (x - 2 y) - 3 y (x - 2 y) \\ = & (x - 2 y) (x - 3 y) \end{array}$

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