Question

simplify: $-1.5(2m - 4) + 0.5(6m + 2)$
a. 6
b. 7
c. 4
d. 5

simplify: $a^2 + 3a^2$
a. $4a$
b. $a^3$
c. $4a^2$
d. $3a^2$

which expression is equivalent to $2(x + 3) + 4(x - 2)$?
a. $6x - 2$
b. $6x - 10$
c. $6x + 2$
d. $-6x + 2

Explanation:

First Question: Simplify \(-1.5(2m - 4)+0.5(6m + 2)\)

Step1: Distribute the coefficients

\(-1.5\times2m=-3m\), \(-1.5\times(-4) = 6\), \(0.5\times6m = 3m\), \(0.5\times2=1\)
So the expression becomes \(-3m + 6+3m + 1\)

Step2: Combine like terms

\(-3m+3m = 0\), \(6 + 1=7\)

Step1: Combine like terms

Since both terms have the same variable part \(a^{2}\), we add their coefficients. The coefficient of \(a^{2}\) is \(1\) and of \(3a^{2}\) is \(3\). So \(1 + 3=4\), and the term is \(4a^{2}\)

Step1: Distribute the coefficients

\(2\times x=2x\), \(2\times3 = 6\), \(4\times x=4x\), \(4\times(-2)=-8\)
The expression becomes \(2x + 6+4x-8\)

Step2: Combine like terms

\(2x+4x = 6x\), \(6-8=-2\)
So the simplified expression is \(6x-2\)

Answer:

b. 7

Second Question: Simplify \(a^{2}+3a^{2}\)