Simplify each of the following algebraic expressions by removing grouping symbols.
2x + (5x − 3y)
We have
2x + (5x − 3y)
Since the '+' sign precedes the parentheses, we have to retain the sign of each term in the parentheses when we remove them.
= 2x + 5x  3y
= 7x  3y
Simplify each of the following algebraic expressions by removing grouping symbols.
3x − (y − 2x)
We have
3x − (y − 2x)
Since the '' sign precedes the parentheses, we have to change the sign of each term in the parentheses when we remove them. Therefore, we have
3x − y + 2x
= 5x  y
Simplify each of the following algebraic expressions by removing grouping symbols.
5a − (3b − 2a + 4c)
We have
5a − (3b − 2a + 4c)
Since the '' sign precedes the parentheses, we have to change the sign of each term in the parentheses when we remove them.
= 5a  3b + 2a  4c
= 7a  3b  4c
Simplify each of the following algebraic expressions by removing grouping symbols.
−2 (x^{2} − y^{2} + xy) − 3(x^{2} + y^{2} − xy)
We have
− 2(x^{2} − y^{2} + xy) − 3(x^{2} + y^{2} − xy)
Since the '' sign precedes the parentheses, we have to change the sign of each term in the parentheses when we remove them.
=  2x^{2}^{ }+ 2y^{2}^{ } 2xy  3x^{2}  3y^{2}^{ }+ 3xy
=  2x^{2}^{ } 3x^{2}^{ }+ 2y^{2} 3y^{2}  2xy + 3xy
=  5x^{2}  y^{2} + xy
Simplify each of the following algebraic expressions by removing grouping symbols.
3x + 2y − {x − (2y − 3)}
We have
3x + 2y − {x − (2y − 3)}
First, we have to remove the small brackets (or parentheses): ( ). Then, we have to remove the curly brackets (or braces): { }.
Therefore,
= 3x + 2y − {x − 2y + 3}
= 3x + 2y − x + 2y  3
= 2x + 4y  3
Simplify each of the following algebraic expressions by removing grouping symbols.
5a − {3a − (2 − a) + 4}
We have
5a − {3a − (2 − a) + 4}
First, we have to remove the small brackets (or parentheses): ( ). Then, we have to remove the curly brackets (or braces): { }.
Therefore,
= 5a − {3a − 2 + a + 4}
= 5a − 3a + 2  a  4
= 5a  4a  2
= a  2
Simplify each of the following algebraic expressions by removing grouping symbols.
a − [b − {a − (b − 1) + 3a}]
First we have to remove the parentheses, or small brackets, ( ), then the curly brackets, { }, and then the square brackets [ ].
Therefore, we have
a  [b  {a  (b  1) + 3a}]
= a  [b  {a  b + 1 + 3a}]
= a  [b  {4a  b + 1}]
= a  [b  4a + b  1]
= a  [2b  4a  1]
= a  2b + 4a + 1
= 5a  2b + 1
Simplify each of the following algebraic expressions by removing grouping symbols.
a − [2b − {3a − (2b − 3c)}]
First we have to remove the small brackets, or parentheses, ( ), then the curly brackets, { }, and then the square brackets, [ ].
Therefore, we have
a  [2b  {3a  (2b  3c)}]
= a  [2b  {3a  2b + 3c}]
= a  [2b  3a + 2b  3c]
= a  [4b  3a  3c]
= a  4b + 3a + 3c
= 4a  4b + 3c
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