Question

Like Term Combine and distributive PropertyA).Find the Like Terms and combine them1) 6 + 8 a^2 + 10a –9b^2 -9a +11a + 8 b^2 - 11a +12 b^2 -4 + 5a^2B). Use Distributive Property to simplify the expressions 1).6(m+2) – 2(m-2)2).2(4x+3) -53).3(y-3)+2y4).7( Z-2) + 6(-Z+1) –10(6Z +8)

Answer 1

For part A. First you can order the terms according to those that have the same literal part, like this

First those who have a^2 then those who have a, then those who have b^2, then those who have b and finally, those who have no literal part

$\begin{gathered} 6+8a^2+10a-9b^2-9a+11a+8b^2-11a+12b^2-4 \\ \text{ So,} \\ 8a^2+10a-9a+11a-11a-9b^2+8b^2+12b^2+6-4 \end{gathered}$

Now you can add those that have the same literal part

$8a^2+a+11b^2+2$

For part B. First make the product and then add those that have the same literal part

So, for the point 1)

$\begin{gathered} 6\mleft(m+2\mright)-2\mleft(m-2\mright)=6m+12-2m+4 \\ \text{ Add those that have the same literal part} \\ 6(m+2)-2(m-2)=4m+16 \end{gathered}$

for the point 2)

$2\mleft(4x+3\mright)-5=8x+6-5=8x+1$

for the point 3)

$3\mleft(y-3\mright)+2y=3y-9+2y=5y-9$

Finally, for the point 4)

$\begin{gathered} 7\mleft(Z-2\mright)+6\mleft(-Z+1\mright)-10\mleft(6Z+8\mright)=7Z-14-6Z+6-60Z-80 \\ 7(Z-2)+6(-Z+1)-10(6Z+8)=-59Z-88 \end{gathered}$