Problem 195 Multiply. $$-8 x\left(x^{2}+2 ... [FREE SOLUTION]

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Chapter 6: Problem 195

Multiply. $$-8 x\left(x^{2}+2 x-15\right)$$

Short Answer

Expert verified

-8x^3 - 16x^2 + 120x

Step by step solution

- Distribute the Multiplicand

Multiply $-8x$ by each term within the parentheses separately. The terms are $x^{2}$, $2x$, and $-15$.

- Multiply by the First Term

Multiply $-8x$ by $x^{2}$: $-8x \times x^{2} = -8x^{3}$.

- Multiply by the Second Term

Multiply $-8x$ by $2x$: $-8x \times 2x = -16x^{2}$.

- Multiply by the Third Term

Multiply $-8x$ by $-15$: $-8x \times -15 = 120x$.

- Combine the Results

Combine all the results to get the final expanded form: $-8x^{3} - 16x^{2} + 120x$.

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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 fundamental concept in algebra that allows you to multiply each term within a parenthesis by a multiplier outside. In this exercise, we multiply \-8x\ by each term in the expression inside the parentheses $x^{2} + 2x - 15$. Here's an easy way to think about it:

\[a(b + c + d) = ab + ac + ad\]
Breaking it down, we distribute the multiplier to every term inside. So, \-8x(x^{2} + 2x - 15)\ becomes:
1. \-8x \times x^{2}\
2. \-8x \times 2x\
3. \-8x \times -15\.
You see, it's not so daunting when you tackle one term at a time!

Algebraic Expressions

An algebraic expression is a combination of numbers, variables, and mathematical operators. In this problem, $x^{2} + 2x - 15$ is our algebraic expression. It's important to familiarize yourself with the structure. Here's what we have:

$x^{2}$: This is a term with a variable raised to the power of 2 (an exponent).
$2x$: This is a term with a variable, which represents '2 times x'.
$-15$: This is a constant term.

We combine these terms and use algebraic rules, such as the distributive property, to manipulate and simplify expressions. This skill is essential for solving equations and tackling many problems in algebra.

Exponents

Exponents are a way to express repeated multiplication of a number by itself. For example, $x^{2}$ means $x \times x$. Learning how to work with exponents is crucial in algebra. They follow specific rules when multiplied by other terms.

In this exercise, let's consider \-8x \times x^{2}\:
\

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91影视

Multiply. $$-8 x\left(x^{2}+2 x-15\right)$$

Short Answer

Step by step solution

- Distribute the Multiplicand

- Multiply by the First Term

- Multiply by the Second Term

- Multiply by the Third Term

- Combine the Results

Key Concepts

Distributive Property

Algebraic Expressions

Exponents

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