Problem 29 Simplify each expression. $$ ... [FREE SOLUTION]

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Chapter 0: Problem 29

Simplify each expression. $$ 2(x-3 y+2 z) $$

Short Answer

Expert verified

2x - 6y + 4z

Step by step solution

Distribute the constant

Distribute the constant 2 to each term inside the parentheses.

Multiply each term

Multiply 2 by each term inside the parentheses: o 2 times x gives 2x o 2 times -3y gives -6y o 2 times 2z gives 4z

Write the simplified expression

Combine all the terms after the multiplication to form the simplified expression: 2x - 6y + 4z.

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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 us to simplify expressions and solve equations more easily. It states that for any numbers or algebraic expressions a, b, and c, the following is true: \[ a(b + c) = ab + ac \].
What this means is that you can distribute the multiplication of 'a' to both 'b' and 'c'. For example, when you have an expression like 2(x - 3y + 2z), you can use the distributive property to break this down.
Distribute the 2 to each term inside the parentheses. You will get:

2 times x
2 times -3y
2 times 2z

This way, the distributive property helps to make complex expressions simpler and more manageable.

Multiplication of Constants

Multiplying constants is a straightforward yet important step in simplifying algebraic expressions. Here, we continue from the last step where we used the distributive property. Remember our example expression: 2(x - 3y + 2z). We've already distributed the 2. Now, we need to perform the multiplication:

2 multiplied by x gives 2x
2 multiplied by -3y gives -6y
2 multiplied by 2z gives 4z

So, each term inside the parentheses becomes multiplied by the constant outside, resulting in 2x, -6y, and 4z respectively. Simple multiplication with constants helps convert an expression into a more workable form.

Combining Like Terms

Combining like terms is a key step in simplifying algebraic expressions. Like terms are terms that have identical variable parts raised to the same power. For instance, in our example 2(x - 3y + 2z), once the distribution is done and we have 2x - 6y + 4z, we must check if there are any like terms to combine. Since all terms (2x, -6y, and 4z) have different variables, they are not like terms.
In cases where you do have like terms, such as 3x + 2x, you add the coefficients to get 5x. This process of combining helps to further simplify expressions. Identifying and grouping like terms makes equations easier to solve and expressions clearer to understand.

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91影视

Simplify each expression. $$ 2(x-3 y+2 z) $$

Short Answer

Step by step solution

Distribute the constant

Multiply each term

Write the simplified expression

Key Concepts

Distributive Property

Multiplication of Constants

Combining Like Terms

One App. One Place for Learning.

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