Simplify The Expression $-4 X^2(3 X - 7$\].A. $-12 X^3 + 28$ B. $-12 X^3 + 28 X^2$ C. $-12 X^3 - 28$ D. $-12 X^3 - 28 X^2$

Introduction

In algebra, simplifying expressions is a crucial skill that helps us solve equations and manipulate mathematical statements. In this article, we will focus on simplifying the expression $-4 x^2(3 x - 7)$. We will break down the expression into smaller parts, apply the distributive property, and combine like terms to arrive at the simplified form.

Understanding the Expression

The given expression is $-4 x^2(3 x - 7)$. This expression consists of two main parts: $-4 x^2$ and $(3 x - 7)$. The first part is a monomial, which is a single term with a variable and a coefficient. The second part is a binomial, which is a polynomial with two terms.

Applying the Distributive Property

To simplify the expression, we need to apply the distributive property, which states that for any real numbers $a$, $b$, and $c$, $a(b + c) = ab + ac$. In this case, we can apply the distributive property to the expression $-4 x^2(3 x - 7)$.

-4 x^2(3 x - 7) = -4 x^2(3 x) - 4 x^2(-7)

Simplifying the Expression

Now that we have applied the distributive property, we can simplify the expression further. We can start by simplifying the first term, $-4 x^2(3 x)$.

-4 x^2(3 x) = -12 x^3

Next, we can simplify the second term, $-4 x^2(-7)$.

-4 x^2(-7) = 28 x^2

Combining Like Terms

Now that we have simplified both terms, we can combine them to arrive at the final simplified form.

-12 x^3 + 28 x^2

Conclusion

In this article, we simplified the expression $-4 x^2(3 x - 7)$ by applying the distributive property and combining like terms. We arrived at the final simplified form, $-12 x^3 + 28 x^2$. This expression is the correct answer to the given problem.

Answer

The correct answer is:

• A. $-12 x^3 + 28 x^2$

Explanation

The correct answer is $-12 x^3 + 28 x^2$ because we applied the distributive property and combined like terms to simplify the expression. The other options, $-12 x^3 + 28$, $-12 x^3 - 28$, and $-12 x^3 - 28 x^2$, are incorrect because they do not accurately represent the simplified form of the expression.

Tips and Tricks

• When simplifying expressions, always apply the distributive property to expand the expression.
• Combine like terms to simplify the expression further.
• Check your work by plugging in values or using a calculator to verify the simplified form.

Practice Problems

• Simplify the expression $2 x^2(3 x + 4)$.
• Simplify the expression $-3 x^2(2 x - 5)$.
• Simplify the expression $x^2(2 x + 3)$.

Answer Key

• $6 x^3 + 8 x^2$
• $-6 x^3 + 15 x^2$
• $2 x^3 + 3 x^2$

Conclusion

Simplifying expressions is an essential skill in algebra that helps us solve equations and manipulate mathematical statements. By applying the distributive property and combining like terms, we can simplify expressions and arrive at the final simplified form. In this article, we simplified the expression $-4 x^2(3 x - 7)$ and arrived at the correct answer, $-12 x^3 + 28 x^2$. We also provided tips and tricks for simplifying expressions and practice problems for readers to try.