Identify the coefficients and variables of the following terms, and simplify the given expressions.

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions to the problems:

A. Identify the coefficients and variables of the following terms:

1. For the expression $\frac{3}{4}X - y$ :

For the term $\frac{3}{4}X$ : Coefficient: $\boxed{\frac{3}{4}}$ Variable: $\boxed{X}$
For the term $-y$ : Coefficient: $\boxed{-1}$ Variable: $\boxed{y}$

2. For the term $\frac{X}{2}$ :
Coefficient: $\boxed{\frac{1}{2}}$
Variable: $\boxed{X}$

3. For the term $12xy$ :
Coefficient: $\boxed{12}$
Variable: $\boxed{xy}$

B. Simplify the following:

1. Simplify $p + 10p - 7p - 8p + 12p$ .

Combine the coefficients of the like terms.
$(1 + 10 - 7 - 8 + 12)p$
Perform the arithmetic operation on the coefficients.
$(11 - 7 - 8 + 12)p$ $(4 - 8 + 12)p$ $(-4 + 12)p$ $8p$
The simplified expression is $\boxed{8p}$ .

2. Simplify $M - 7M - 3M + 8M$ .
Combine the coefficients of the like terms.
$(1 - 7 - 3 + 8)M$
Perform the arithmetic operation on the coefficients.
$(-6 - 3 + 8)M$ $(-9 + 8)M$ $-1M$
The simplified expression is $\boxed{-M}$ .

3. Simplify $3X - X + 7M - 8M$ .
Group the like terms together.
$(3X - X) + (7M - 8M)$
Combine the coefficients for each group of like terms.
$(3 - 1)X + (7 - 8)M$ $2X + (-1)M$ $2X - M$
The simplified expression is $\boxed{2X - M}$ .

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