Problem 56 Simplify. $$-5\left(3 x^{2}\ri... [FREE SOLUTION]

Chapter 4: Problem 56

Simplify. $$-5\left(3 x^{2}\right)$$

Short Answer

Expert verified

-15x^2

Step by step solution

Apply the distributive property

Apply the distributive property by multiplying -5 by each term inside the parentheses. In this case, we only have one term, 3x^2. Therefore, the expression simplifies to -5 * 3x^2.

Simplify

Perform the multiplication. -5 * 3 equals -15, thus the expression simplifies to -15x^2.

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Key Concepts

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

Simplifying Expressions

In mathematics, simplifying expressions is a vital skill that involves transforming an algebraic expression into its easiest possible form. The goal is to make the expression as straightforward as possible.
For instance, in the given expression $-5(3x^2)$, we use operations such as the distributive property to streamline the expression.
To simplify expressions:

Remove parentheses by applying the distributive property.
Combine like terms if available.
Reduce coefficients where possible by performing multiplication or division.

In our example, multiplying $-5$ by $3x^2$ eliminates the parentheses and simplifies it to $-15x^2$. This process clears away unnecessary complexity, helping you understand the expression better.

Algebraic Multiplication

Algebraic multiplication involves multiplying coefficients (or constants) and variables within an algebraic expression. This can involve integers, fractions, or decimals. It's crucial to correctly apply multiplication principles to prevent errors.
When dealing with algebraic multiplication, follow these steps:

Multiply the numeric coefficients directly.
Next, multiply and combine any similar variables.

For $-5(3x^2)$, the coefficients $-5$ and $3$ multiply to become $-15$. Here, since $x^2$ has no similar variable to multiply, it remains unchanged as $-15x^2$. Always execute the multiplication thoroughly to make sure that all parts of the expression are simplified properly.

Exponents

Exponents are shorthand notation to represent repeated multiplication of the same factor. In the expression $x^2$, the variable $x$ is multiplied by itself twice.
Exponents offer a compact way to handle large numbers that result from repeated multiplications, and they obey specific rules:

When multiplying, add exponents if the base numbers are the same.
For instance: $x^m \times x^n = x^{m+n}$.
When raising power to power, multiply the exponents. $(x^m)^n = x^{m \cdot n}$.

In our expression, $3x^2$, the exponent simply tells us that the variable $x$ is squared. When distributing with $-5$, it remains unaffected unless further operations specify a change. Understanding exponents ensures accurate simplification of polynomial expressions.

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91影视

Simplify. $$-5\left(3 x^{2}\right)$$

Short Answer

Step by step solution

Apply the distributive property

Simplify

Key Concepts

Simplifying Expressions

Algebraic Multiplication

Exponents

One App. One Place for Learning.

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