Problem 52 Find the sum of \(\left(q^{2}+4 ... [FREE SOLUTION]

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Chapter 6: Problem 52

Find the sum of \(\left(q^{2}+4 q+13\right)\) and \(\left(7 q^{3}-3\right)\).

Short Answer

Expert verified

The sum is \[ 7q^{3} + q^{2} + 4q + 10 \]

Step by step solution

Write down the given expressions

The given expressions are \[ q^{2} + 4q + 13 \] and \[ 7q^{3} - 3 \] respectively.

Set up the addition of the expressions

To find the sum, place the expressions in an addition setup: \[ (q^{2} + 4q + 13) + (7q^{3} - 3) \]

Combine like terms

Combine the like terms from the expressions. In this case, there are no like terms between the two expressions, so the sum is simply: \[ 7q^{3} + q^{2} + 4q + 13 - 3 \]

Simplify the expression

Simplify the combined expression by combining the constants 13 and -3: \[ 7q^{3} + q^{2} + 4q + 10 \]

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Key Concepts

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

combining like terms

Combining like terms is a fundamental part of working with algebraic expressions. To combine like terms, you need to focus on terms that have the same variable raised to the same power. For instance, in the expression \(2x + 3 + x - 5\), the like terms are \(2x\) and \(x\).

By adding the coefficients of the like terms, you get \(3x\).

Similarly, the constants \(3\) and \(-5\) can be combined to \text{-2}\. When there are no like terms, you just rearrange the terms. This step is crucial for simplifying any algebraic expression.

simplifying expressions

Simplifying expressions involves both combining like terms and reducing the expression to its most straightforward form. After combining like terms, you need to ensure that there are no unnecessary parentheses or redundant terms. Simplifying also means making sure the coefficients and constants are in their simplest forms.

For instance, in the example \( (q^{2} + 4q + 13) + (7q^{3} - 3) \), after combining the terms, you get \( 7q^{3} + q^{2} + 4q + 10 \), which is the simplest form of this expression.

algebraic expressions

Algebraic expressions are mathematical phrases that can include numbers, variables, and operations. Variables represent unknown values and can be manipulated to solve equations or create expressions.

For example, in the given problem, \( q^{2} + 4q + 13 \) and \( 7q^{3} - 3 \) are both algebraic expressions. They can be added, subtracted, multiplied, etc., to form new expressions.

Mastering how to work with algebraic expressions by understanding operations and simplifying techniques is crucial for solving algebra problems efficiently. Every algebraic operation relies on the basic principles of arithmetic but includes variables as placeholders.

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91影视

Find the sum of \(\left(q^{2}+4 q+13\right)\) and \(\left(7 q^{3}-3\right)\).

Short Answer

Step by step solution

Write down the given expressions

Set up the addition of the expressions

Combine like terms

Simplify the expression

Key Concepts

combining like terms

simplifying expressions

algebraic expressions

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