Question

1. write the expression in standard form.

$(4f - 3 + 2q) - (-4q + 2)$

1. find the result when $5m + 2$ is subtracted from $9m$.

1. write the expression in standard form.

$27h + 3h$

Explanation:

Problem 1

Step1: Remove parentheses

To remove the parentheses, we distribute the negative sign to the terms inside the second parentheses:
$$(4f - 3 + 2g) - (-4g + 2) = 4f - 3 + 2g + 4g - 2$$

Step2: Combine like terms

Combine the constant terms and the terms with \( g \):

• For the constant terms: \( -3 - 2 = -5 \)
• For the terms with \( g \): \( 2g + 4g = 6g \)

The term with \( f \) remains as is.

So, the expression becomes:
$$4f + 6g - 5$$

Step1: Translate the problem into an expression

"Subtract \( 5m + 2 \) from \( 9m \)" means \( 9m - (5m + 2) \).

Step2: Remove parentheses and combine like terms

Distribute the negative sign:
$$9m - 5m - 2$$

Combine the terms with \( m \):
\( 9m - 5m = 4m \)

So, the result is \( 4m - 2 \).

Step1: Combine like terms

The expression \( 27h + 3h \) has like terms (both have the variable \( h \)). Combine their coefficients:
\( 27 + 3 = 30 \)

So, \( 27h + 3h = 30h \).

Answer:

\( 4f + 6g - 5 \)

Problem 2