Problem 75 Simplify. $$(-2 x)\left(-3 x y... [FREE SOLUTION]

Chapter 9: Problem 75

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

Short Answer

Expert verified

The simplified form of the given expression is $ -18x^{3}y^{4} $

Step by step solution

Expand Inner Parentheses

The exponent applies to everything within the parentheses. Raise each factor within the parentheses to the given power: $ (-3)^2, (x)^2, \text{ and } (y^{2})^2 $ respectively. The expression becomes $ -2x * 9x^{2}y^{4} $

Simplify

Multiply the like terms together (the coefficients and then the variables separately) following the rules of coefficients multiplication and variable exponents addition, the expression then simplifies to $ -18x^{3}y^{4} $

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Key Concepts

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

Exponentiation

Exponentiation is an essential concept in algebra. It involves raising a number or an expression to a power. In our example, $(-3xy^2)^2$, the entire expression inside the parentheses is squared. This means each component inside the parentheses is raised to the power of 2.

Numbers: $(-3)^2 = 9$, because multiplying $-3$ by itself results in 9.
Variables: For $x$, $x^2$ represents multiplying $x$ by itself. And for $y^2$, $(y^2)^2 = y^4$, by multiplying the powers which gives us 2 * 2 = 4.

Exponentiation makes calculations concise and manageable in algebra, eliminating the need for repeated multiplication.

Multiplication of Polynomials

When multiplying polynomials, you use the distributive property to combine all terms.This concept involves both coefficients (numbers) and variables.
In our problem, after expanding the squared expression, we have $-2x * 9x^2y^4$. Here's how:

Coefficients: Multiply $-2$ and $9$ to get $-18$.
Variables: Multiply the like terms. For instance, $x * x^2 = x^{3}$ because 1 + 2 = 3 (add exponents).

By carefully combining both coefficients and variables, the expression simplifies effectively, following the standard polynomial multiplication rules.

Simplifying Expressions

Simplifying expressions is about combining like terms to present a shorter, clearer form.Each individual step should be checked to ensure accuracy.
Starting with $-2x * 9x^2y^4$, the process involved:

Multiply Coefficients: $-2 * 9 = -18$.
Variables: Combine like terms by adding their exponents, such as $x * x^2 = x^3$ and $y^4$ remains the same since there are no other 'y' terms to combine.

The expression simplifies to $-18x^3y^4$, showcasing how efficient simplification leads to a cleaner, more understandable result. This is crucial for solving real-world problems with algebraic expressions.

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91影视

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

Short Answer

Step by step solution

Expand Inner Parentheses

Simplify

Key Concepts

Exponentiation

Multiplication of Polynomials

Simplifying Expressions

One App. One Place for Learning.

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