Simplify the algebraic expressions: 4(m+n) − 3(2m-n) + (m−3n) and (K-2e)/(2) − (K-3e)/(8).

Question

ScanSolve AI Tutor · Accepted Answer

Let's simplify these algebraic expressions.

: Simplify $4(m+n) - 3(2m-n) + (m-3n)$

Distribute the coefficients into the parentheses.
$4m + 4n - 6m + 3n + m - 3n$
Group the like terms together.
$(4m - 6m + m) + (4n + 3n - 3n)$
Combine the like terms.
$(4 - 6 + 1)m + (4 + 3 - 3)n$ $(-2 + 1)m + (7 - 3)n$ $-1m + 4n$ $\boxed{-m + 4n}$
: Express $\frac{K-2e}{2} - \frac{K-3e}{8}$ as a single fraction in simplest form.
Find the least common denominator (LCD) for the fractions.
The denominators are 2 and 8. The LCD is 8.
To get a denominator of 8 for the first fraction, multiply it by $\frac{4}{4}$ .
$\frac{4(K-2e)}{4 \cdot 2} - \frac{K-3e}{8}$ $\frac{4(K-2e)}{8} - \frac{K-3e}{8}$
Combine the numerators over the common denominator.
Remember to distribute the negative sign to all terms in the second numerator.
$\frac{4(K-2e) - (K-3e)}{8}$
Distribute the 4 and the negative sign in the numerator.
$\frac{4K - 8e - K + 3e}{8}$
Combine like terms in the numerator.
$\frac{(4K - K) + (-8e + 3e)}{8}$ $\frac{3K - 5e}{8}$ $\boxed{\frac{3K - 5e}{8}}$

Simplify the algebraic expressions: 4(m+n) - 3(2m-n) + (m-3n) and (K-2e)/(2) - (K-3e)/(8).