Sure, let's simplify each expression step by step by combining like terms.
### a) Simplify [tex]\( 4a + 2b + 3a + 4b \)[/tex]
1. Combine the like terms involving [tex]\(a\)[/tex]:
[tex]\[
4a + 3a = 7a
\][/tex]
2. Combine the like terms involving [tex]\(b\)[/tex]:
[tex]\[
2b + 4b = 6b
\][/tex]
Thus, the simplified expression is:
[tex]\[
7a + 6b
\][/tex]
### b) Simplify [tex]\( a + b + 2a - b \)[/tex]
1. Combine the like terms involving [tex]\(a\)[/tex]:
[tex]\[
a + 2a = 3a
\][/tex]
2. Combine the like terms involving [tex]\(b\)[/tex]:
[tex]\[
b - b = 0
\][/tex]
Thus, the simplified expression is:
[tex]\[
3a
\][/tex]
### c) Simplify [tex]\( c + 3d - 2c + 2d \)[/tex]
1. Combine the like terms involving [tex]\(c\)[/tex]:
[tex]\[
c - 2c = -c
\][/tex]
2. Combine the like terms involving [tex]\(d\)[/tex]:
[tex]\[
3d + 2d = 5d
\][/tex]
Thus, the simplified expression is:
[tex]\[
-c + 5d
\][/tex]
### d) Simplify [tex]\( 2p - 3q - p + 4q \)[/tex]
1. Combine the like terms involving [tex]\(p\)[/tex]:
[tex]\[
2p - p = p
\][/tex]
2. Combine the like terms involving [tex]\(q\)[/tex]:
[tex]\[
-3q + 4q = q
\][/tex]
Thus, the simplified expression is:
[tex]\[
p + q
\][/tex]
### e) Simplify [tex]\( -3x + 5y + 5x - 3y \)[/tex]
1. Combine the like terms involving [tex]\(x\)[/tex]:
[tex]\[
-3x + 5x = 2x
\][/tex]
2. Combine the like terms involving [tex]\(y\)[/tex]:
[tex]\[
5y - 3y = 2y
\][/tex]
Thus, the simplified expression is:
[tex]\[
2x + 2y
\][/tex]
### f) Simplify [tex]\( 4f + 2g + h + 2f - g \)[/tex]
1. Combine the like terms involving [tex]\(f\)[/tex]:
[tex]\[
4f + 2f = 6f
\][/tex]
2. Combine the like terms involving [tex]\(g\)[/tex]:
[tex]\[
2g - g = g
\][/tex]
3. The term [tex]\(h\)[/tex] remains as it is since there are no other [tex]\(h\)[/tex] terms to combine with.
Thus, the simplified expression is:
[tex]\[
6f + g + h
\][/tex]
Here are the simplified expressions for each part:
a) [tex]\(7a + 6b\)[/tex]
b) [tex]\(3a\)[/tex]
c) [tex]\(-c + 5d\)[/tex]
d) [tex]\(p + q\)[/tex]
e) [tex]\(2x + 2y\)[/tex]
f) [tex]\(6f + g + h\)[/tex]
