Problem 19 Multiply. $$ -2(5 x 2-3 x+4)... [FREE SOLUTION]

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Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 5: Problem 19

Multiply. $$ -2(5 x 2-3 x+4) $$

Short Answer

Expert verified

The result is \$-10x^2 + 6x - 8\$.

Step by step solution

Apply the Distributive Property

Start by applying the distributive property to each term inside the parentheses. This means multiplying $-2$ by each term within $5x^2 - 3x + 4$.

Multiply the First Term

Multiply $-2$ by $5x^2$, which results in $-10x^2$. So the expression becomes $-10x^2$.

Multiply the Second Term

Multiply $-2$ by $-3x$, resulting in $6x$ (since negative times negative is positive). Now the expression is $-10x^2 + 6x$.

Multiply the Third Term

Multiply $-2$ by $4$, which gives you $-8$. The expression is now $-10x^2 + 6x - 8$.

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Key Concepts

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

Polynomial Multiplication

Polynomial multiplication involves expanding expressions where terms are multiplied together. Each term in a polynomial is multiplied separately, and this is usually done using the distributive property. In the original example, the polynomial is $5x^2 - 3x + 4$ and it needs to be multiplied by $-2$. The distributive property is applied by multiplying $-2$ by each term in the polynomial:

First, multiply $-2$ by $5x^2$ to get $-10x^2$.
Then, multiply $-2$ by $-3x$ which results in $6x$.
Lastly, multiply $-2$ by $4$ to obtain $-8$.

This process results in a new polynomial $-10x^2 + 6x - 8$. Remember that each term in the polynomial needs to be multiplied separately and then combined to achieve the final expression.

Negative Numbers

Working with negative numbers can sometimes be tricky, but they follow consistent rules. The most important rule is that multiplying two negative numbers results in a positive number. In our example:

When $-2$ is multiplied by $-3x$, the result is $6x$, because negative times negative equals positive.

Similarly, multiplying a positive number by a negative number results in a negative number.

For example, multiplying $-2$ by $4$ results in $-8$.

Understanding these basic principles about negative numbers will help you in many algebraic expressions and equation problems.

Algebraic Expressions

An algebraic expression is a mathematical phrase involving numbers, variables, and operations. In algebraic expressions, terms are combined using addition or subtraction. Each term can be a number, a variable, or a combination of both, known as a coefficient for the variable. Let's look at the expression in the exercise:

$5x^2$ is a term where $5$ is the coefficient and $x^2$ is the variable.
$-3x$ is another term, with $-3$ as the coefficient and $x$ as the variable.
$4$ is a constant term, meaning it doesn't change with the variable $x$.

Expressions like these are the building blocks in algebra, enabling us to formulate and solve equations that represent various mathematical relationships and real-life scenarios.

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91影视

Multiply. $$ -2(5 x 2-3 x+4) $$

Short Answer

Step by step solution

Apply the Distributive Property

Multiply the First Term

Multiply the Second Term

Multiply the Third Term

Key Concepts

Polynomial Multiplication

Negative Numbers

Algebraic Expressions

One App. One Place for Learning.

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