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 \(-\frac{9}{7} n+1\).