Write all the terms of the algebraic expression 5x³ – 3xy² + 7xy – 8. Also, write its constant term.

Understand the Problem

The question is asking to identify and list all the individual terms of the given algebraic expression, as well as to specify which term is the constant term.

Answer

The terms are $5x^3$, $-3xy^2$, $7xy$, $-8$; the constant term is $-8$.

Steps to Solve

Identify the terms in the expression

The given algebraic expression is $5x^3 - 3xy^2 + 7xy - 8$.

To identify the terms, we separate each part of the expression:

The first term is $5x^3$.
The second term is $-3xy^2$.
The third term is $7xy$.
The fourth term is $-8$.

List all the terms

We can now list the identified terms in a comprehensive way:

$5x^3$
$-3xy^2$
$7xy$
$-8$

Determine the constant term

The constant term is the term that does not have any variable (like $x$ or $y$).

From the list, the constant term is $-8$.

The terms of the algebraic expression are: $5x^3$, $-3xy^2$, $7xy$, $-8$.

The constant term is $-8$.

More Information

The constant term in an algebraic expression is critical because it represents the value of the expression when all the variables are set to zero. In this case, when $x = 0$ and $y = 0$, the expression simplifies to $-8$.

Tips

Forgetting to include all terms: Make sure to read the expression carefully and list each term.
Misidentifying the constant term: Remember, the constant term has no variables associated with it.

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