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Chapter 4: Problem 7

Combining like terms in \(-3 x y-2 x y+5 x y\) gives _____________.

Short Answer

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Step by step solution

01

- Identify Like Terms

To combine like terms, first identify which terms are alike. Here, the terms (-3xy), (-2xy), and (5xy) are all like terms because they all contain the same variables with the same exponents.
02

- Combine Coefficients

Next, add or subtract the coefficients of these like terms. The coefficients are -3, -2, and 5. Combine them as follows: (-3) + (-2) + 5
03

- Perform the Arithmetic

Calculate the result of the combined coefficients: (-3) + (-2) = -5 Next, (-5) + 5 = 0
04

- Write the Simplified Expression

Since the combined coefficient is 0, the simplified expression of the terms is 0xy, which simplifies to 0.

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Key Concepts

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

coefficients
In algebra, coefficients are numbers that are multiplied by variables in an expression. For example, in the term \(3x\), the number 3 is the coefficient. Coefficients can be positive or negative numbers and can include fractions and decimals. In the original exercise, the coefficients are -3, -2, and 5. To combine these terms, we'll focus on these coefficients and perform arithmetic operations on them while keeping the variables the same.
like terms
Like terms in algebra are terms that have the same variables raised to the same powers. They can have different coefficients, but the variable part must be identical. In the exercise, \(-3xy, -2xy,\) and \(5xy\) are all like terms because they all contain the variable combination \(xy\). This similarity allows us to add or subtract their coefficients, making the expression simpler. Identifying like terms is crucial for simplifying algebraic expressions.
simplified expressions
Simplified expressions are algebraic expressions that have been reduced to their simplest form. This includes combining like terms and performing any possible arithmetic operations. For our exercise, combining the like terms \(-3xy, -2xy,\) and \(5xy\) gave us a coefficient of 0 for \(xy\). Therefore, the simplified expression is 0. Simplification helps make expressions easier to understand and solve.
variables
Variables are symbols used to represent unknown or changeable values in algebra. They are usually letters like \(x, y,\) or \(z\). In our example, \(x\) and \(y\) are the variables. These variables stay the same while we combine the coefficients of their terms. Understanding how to work with variables, including keeping their powers consistent, is essential for combining like terms correctly.

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Most popular questions from this chapter

In 2017 , the fastest computer in the United States could handle 17.59 quadrillion calculations per second. (Hint: 1 quadrillion \(=1 \times 10^{15}\).) How many calculations could it perform per minute? Per hour? (Data from www.top500.org)

Find each product. Recall that \(a^{2}=a \cdot a\) and \(a^{3}=a^{2} \cdot a\). $$ (b-10)(b+10) $$

Find each product. Recall that \(a^{2}=a \cdot a\) and \(a^{3}=a^{2} \cdot a\). $$ \left(3 p^{2}+\frac{5}{4} q\right)\left(2 p^{2}-\frac{5}{3} q\right) $$

Find each product. $$ (2 m-3 n)(m+5 n) $$

Find each product. Recall that \(a^{2}=a \cdot a\) and \(a^{3}=a^{2} \cdot a\). $$ 7(4 m-3)(2 m+1) $$
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