Hey there! We receieved your request
Stay Tuned as we are going to contact you within 1 Hour
One of our academic counsellors will contact you within 1 working day.
Click to Chat
1800-5470-145
+91 7353221155
Use Coupon: CART20 and get 20% off on all online Study Material
Complete Your Registration (Step 2 of 2 )
Sit and relax as our customer representative will contact you within 1 business day
OTP to be sent to Change
Simplify, the algebraic expressions by removing grouping symbols.
2x + (5x – 3y)
We have
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
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
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
-2(x2 - y2 + xy) - 3(x2 +y2 - xy)
- 2(x2 - y2 + xy) - 3(x2 +y2 - xy)
= -2x2 + 2y2 - 2xy - 3x2 - 3y2 + 3xy
= -2x2 - 3x2 + 2y2 - 3y2 - 2xy + 3xy
= -5x2 - y2 + xy
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
5a – {3a – (2 – a) + 4}
= 5a – {3a – 2 + a + 4}
= 5a – 3a + 2 – a – 4
= 5a – 4a – 2
= a – 2
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 – {4a – b + 1}]
= a – [b – 4a + b – 1]
= a – [2b – 4a – 1]
= a – 2b + 4a + 1
= 5a – 2b + 1
a – [2b – {3a – (2b – 3c)}]
First we have to remove the small brackets, or parentheses, ( ), then the curly brackets, { }, and then the square brackets, [ ].
= a – [2b – {3a – 2b + 3c}]
= a – [2b – 3a + 2b – 3c]
= a – [4b – 3a – 3c]
= a – 4b + 3a + 3c
= 4a – 4b + 3c
-x + [5y – {2x – (3y – 5x)}]
First we have to remove the small brackets, or parentheses, ( ), then the curly brackets { }, and then the square brackets, [ ].
– x + [5y – {2x – (3y – 5x)}]
= – x + [5y – {2x – 3y + 5x)]
= – x + [5y – {7x – 3y}]
= – x + [5y – 7x + 3y]
= – x + [8y – 7x]
= – x + 8y – 7x
= – 8x + 8y
2a – [4b – {4a – 3(2a – b)}]
= 2a – [4b – {4a – 6a + 3b}]
= 2a – [4b – {- 2a + 3b}]
= 2a – [4b + 2a – 3b]
= 2a – [b + 2a]
= 2a – b – 2a
= – b
-a – [a + {a + b – 2a – (a – 2b)} - b]
– a – [a + {a + b – 2a – (a – 2b)} – b]
= – a – [a + {a + b – 2a – a + 2b} – b]
= – a – [a + {- 2a + 3b} – b]
= – a – [a – 2a + 3b – b]
= – a – [- a + 2b]
= – a + a – 2b
= – 2b
2x – 3y – [3x – 2y -{x – z – (x – 2y)}]
2x – 3y – [3x – 2y – {x – z – (x – 2y)})
= 2x – 3y – [3x – 2y – {x – z – x + 2y}]
= 2x – 3y – [3x – 2y – {- z + 2y}]
= 2x – 3y – [3x – 2y + z – 2y]
= 2x – 3y – [3x – 4y + z]
= 2x – 3y – 3x + 4y – z
= - x + y – z
5 + [x – {2y – (6x + y – 4) + 2x} – {x – (y – 2)}]
= 5 + [x – {2y – 6x – y + 4 + 2x} – {x – y + 2}]
= 5 + [x – {y – 4x + 4} – {x – y + 2}]
= 5 + [x – y + 4x – 4 – x + y – 2]
= 5 + [4x – 6]
= 5 + 4x – 6
= 4x – 1
x2 - [3x + [2x - (x2 - 1)] + 2]
= x2 - [3x + [2x - x2 + 1] + 2]
= x2 - [3x + 2x - x2 + 1 + 2]
= x2 - [5x - x2 + 3]
= x2 - 5x + x2 - 3
= 2x2 - 5x - 3
20 - [5xy + 3[x2 - (xy - y) - (x - y)]]
= 20 - [5xy + 3[x2 – xy + y – x + y]]
= 20 - [5xy + 3[x2 – xy + 2y - x]]
= 20 - [5xy + 3x2 - 3xy + 6y - 3x]
= 20 - [2xy + 3x2 + 6y - 3x]
= 20 - 2xy - 3x2 - 6y + 3x
= - 3x2 - 2xy - 6y + 3x + 20
85 – [12x – 7(8x – 3) – 2{10x – 5(2 – 4x)}]
= 85 – [12x – 56x + 21 – 2{10x – 10 + 20x}]
= 85 – [12x – 56x + 21 – 2{30x – 10}]
= 85 – [12x – 56x + 21 – 60x + 20]
= 85 – [12x – 116x + 41]
= 85 – [- 104x + 41]
= 85 + 104x – 41
= 44 + 104x
xy[yz – zx – {yx – (3y – xz) – (xy – zy)}]
xy – [yz – zx – {yx – (3y – xz) – (xy – zy)}]
= xy – [yz – zx – {yx – 3y + xz – xy + zy}]
= xy – [yz – zx – {- 3y + xz + zy}]
= xy – [yz – zx + 3y – xz – zy]
= xy – [- zx + 3y – xz]
= xy – [- 2zx + 3y]
= xy + 2xz – 3y
Get your questions answered by the expert for free
You will get reply from our expert in sometime.
We will notify you when Our expert answers your question. To View your Question
Chapter 7: Algebraic Expressions Exercise –...