Question

Subtract. $$ \left(3 a 3+5 a_{2}-2\right)-(a 3-a+8) $$

   Subtract.
$$
\left(3 a 3+5 a_{2}-2\right)-(a 3-a+8)
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 5, Problem 41

Instant Answer

Solved by Expert James Kiss

01/29/2022

Step 1

This changes the sign of each term. $$ (3a^3+5a^2-2)-(a^3-a+8) = 3a^3+5a^2-2-a^3+a-8 $$ Show more…

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Subtract. $$ \left(3 a 3+5 a_{2}-2\right)-(a 3-a+8) $$

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Key Concepts

Polynomial Arithmetic

This concept involves performing operations such as addition, subtraction, and multiplication on expressions that consist of variables raised to various powers and their coefficients. It includes managing the structure of polynomials when combining terms or applying operations across the entire expression.

Distributive Property

This key concept states that a factor outside parentheses multiplies each term within the parentheses. When subtracting polynomials, it is especially important to distribute the negative sign across all terms in the subtracted polynomial to change their signs appropriately.

Combining Like Terms

After applying the distributive property, like terms—terms that have the same variable raised to the same power—can be combined by adding or subtracting their coefficients. This step simplifies the polynomial into its most reduced form.

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