Problem 175 Multiply. $$(2 y-9) y$$... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 10: Problem 175

Multiply. $$(2 y-9) y$$

Short Answer

Expert verified

The result is $2y^2 - 9y$.

Step by step solution

Identify the expression

The given expression to multiply is $ (2y - 9) y $.

Distribute the y

Apply the distributive property to multiply each term inside the parenthesis by y. $(2y - 9)y = (2y \times y) - (9 \times y)$

Multiply each term

First, multiply $2y \times y = 2y^2$. Then, multiply $-9 \times y = -9y$.

Combine the terms

Combine the results from the previous step to obtain the final expression: $2y^2 - 9y$.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

distributive property

The distributive property is a key concept in algebra that simplifies expressions by multiplying a single term by each term inside a parenthesis.
In our exercise, we have the expression $ (2y - 9) y $. To simplify this using the distributive property, we multiply $ y $ by each term inside the parenthesis separately.
Think of the distributive property as spreading out the multiplication over addition or subtraction.

Here, we distribute the $ y $ to both $ 2y $ and $ -9 $ as follows: \[(2y - 9)y = (2y) * y + (-9) * y \].
This simplifies our equation for easier handling.

polynomials

Polynomials are expressions made up of variables and coefficients. They consist of terms which include a variable raised to a power and a coefficient.
In our exercise, $ 2y - 9 $ is a polynomial with two terms.
One term includes a variable $ y $ and the other one is a constant.
This type of polynomial is a binomial, which specifically means it has exactly two terms.

After applying the distributive property, our terms were $(2y * y \text{ and } -9 * y)$.
Each term in a polynomial can vary by its degree, which is the power of the variable.
For instance, $ 2y^2 $ is a second-degree term, and $-9y$ is a first-degree term.

simplifying expressions

Simplifying expressions in algebra means to combine like terms and perform arithmetic operations to put the expression in its simplest form.
In this exercise, once we've used the distributive property to get $(2y^2 - 9y)$, we have our simplified form.
There are no more like terms to combine because $ 2y^2 $ and $-9y$ have different degrees.

If there were similar degrees, like another $ y^2 $, we would add or subtract them to simplify further.
Always perform operations from highest to lowest degree when simplifying polynomials.
By doing so, it ensures your work is organized and correct, giving the final expression in standard form.

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91影视

Multiply. $$(2 y-9) y$$

Short Answer

Step by step solution

Identify the expression

Distribute the y

Multiply each term

Combine the terms

Key Concepts

distributive property

polynomials

simplifying expressions

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