Simplifying Algebraic Expressions

1. Use the distributive property to multiply the $-2.5$ into the parentheses.

= $−2.5(4x−3)$

= $−2.5⋅(4x)+(−2.5)⋅(−3)$

We expanded the expression by multiplying the $-2.5$ by both terms in the parentheses.

=$-10x+7.5$

The expanded expression is $-10x+7.5$.

2. Combine the coefficients of the $b$ terms.

= $=1.3b+7.8−3.2b$

= $(1.3−3.2)⋅b+7.8$

= $(−1.9)⋅b+7.8$

= $−1.9b+7.8$

The simplified expression is $−1.9b+7.8$.

3. Combine the coefficients of the $p$ terms, and combine the constant terms.

= $-\frac{2}{3} p+\frac{1}{5}-1+\frac{5}{6} p$

= $\left(-\frac{2}{3}+\frac{5}{6}\right) \cdot p+\frac{1}{5}-1$

Group the $p$ coefficients together, and group the numeric coefficients together.

= $\left(-\frac{4}{6}+\frac{5}{6}\right) \cdot p+\frac{1}{5}-\frac{5}{5}$

Rewrite $−1$ as $-\frac{5}{5}$ to form common denominators.

= $\left(\frac{1}{6}\right) \cdot p-\frac{4}{5}$

=$\frac{1}{6} p-\frac{4}{5}$

The simplified expression is $\frac{1}{6} p-\frac{4}{5}$.

4. Use the distributive property to multiply the $-3$ into the parentheses.

= $\frac{1}{7}-3\left(\frac{3}{7} n-\frac{2}{7}\right)$

= $\frac{1}{7}+(-3) \cdot\left(\frac{3}{7} n\right)+(-3) \cdot\left(-\frac{2}{7}\right)$

We expanded the expression by multiplying the $-3$ by both terms in the parentheses.

= $\frac{1}{7}-\frac{9}{7} n+\frac{6}{7}$

= $-\frac{9}{7} n+\frac{7}{7}$

We combined the numeric terms.

= $-\frac{9}{7} n+1$

The expanded expression is $-\frac{9}{7} n+1$.