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Sagot :
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]
### 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]
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