Question

Simplify by combining like terms. z² + 8 z² - 2z+5 z .

Answer 1

1. The simplified expression by combining like terms is
`\(9z^2 - 2z + 5\)`.

Step-by-step explanation:

When simplifying the expression
`\(z^2 + 8z^2 - 2z + 5\)`, we combine like terms. Like terms are terms that have the same variable raised to the same power. In this expression, the terms
`\(z^2\)`and
`\(8z^2\)` are like terms because they both have z raised to the power of 2. Combining these terms gives
`\(9z^2\)`. The term -2z stands alone as it does not have any like terms. Finally, the constant term 5 also stands alone. Therefore, the simplified expression is
`\(9z^2 - 2z + 5\)`.

In mathematical expressions, combining like terms involves adding or subtracting coefficients of the same variables raised to the same power. It simplifies the expression, making it more concise and easier to work with. In this case, recognizing that
`\(z^2\)` and
`\(8z^2\)`are like terms allows us to add their coefficients to get \(9z^2\). The final simplified expression
`\(9z^2 - 2z + 5\)` is a clear and concise representation of the given expression after combining like terms.

Answer 2

Combining like terms in z² + 8z² - 2z + 5z, the simplified expression is
`9z^2 + 3z`.

What are like terms?

Like terms are terms in algebraic expressions that have the same variable(s) raised to the same power(s), making them combinable by addition or subtraction.

For example:

• 3x and 5x are like terms because they both have the variable x raised to the power of 1.
• 
  `2y^2` and
  `7y^2` are like terms because they both have the variable y raised to the power of 2.

To simplify the expression
`z^2 + 8z^2 - 2z + 5z`, combine like terms:

Combine the
`\(z^2\)` terms:

`9z^2 - 2z + 5z`

Combine the z terms:

9z² + 3z