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Maths 3 Mark Question

Algebraic Expressions · Maharashtra Board STD 7 (MSBSHSE - Semi English Medium). 27 questions.

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Question 13 Marks
Subtract:
$6 x^3-7 x^2+5 x-3$ from $4-5 x+6 x^2-8 x^3$
Answer
Required expression:
$=\left(4-5 x+6 x^2-8 x^3\right)-\left(6 x^3-7 x^2+5 x-3\right)$
$=4-5 x+6 x^2-8 x^3-6 x^3+7 x^2-5 x+3$
$=-8 x^3-6 x^3+7 x^2+6 x^2-5 x-5 x+3+4$
$=-14 x^3+13 x^2-10 x+7$
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Question 23 Marks
Simplify the following algebraic expressions by removing grouping symbols:
2a - [4b - {4a - 3(2a - b)}]
Answer
First we have to remove the small brackets, or parentheses, (), then the curly brackets, {}, and then the square brackets, [].
Therefore, we have
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
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Question 33 Marks
From,
$x^3-5 x^2+3 x+1$, take away $6 x^2-4 x^3+5+3 x$
Answer
Required expression:
$=\left(x^3-5 x^2+3 x+1\right)-\left(6 x^2-4 x^3+5+3 x\right)$
$=x^3-5 x^2+3 x+1-6 x^2+4 x^3-5-3 x$
$=x^3+4 x^3-5 x^2-6 x^2+1-5$
$=5 x^3-11 x^2-4$
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Question 43 Marks
$7+x-x^2$, take away $9+x+3 x^2+7 x^3$
Answer
Required expression:
$=\left(7+x-x^2\right)-\left(9+x+3 x^2+7 x^3\right)$
$=7+x-x^2-9-x-3 x^2-7 x^3$
$=-7 x^3-x^2-3 x^2+7-9$
$=-7 x^3-4 x^2-2$
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Question 53 Marks
From,
$1-5 y^2$, take away $y^3+7 y^2+y+1$
Answer
Required expression:
$=\left(1-5 y^2\right)-\left(y^3+7 y^2+y+1\right)$
$=1-5 y^2-y^3-7 y^2-y-1$
$=-y^3-5 y^2-7 y^2-y$
$=-y^3-12 y^2-y$
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Question 63 Marks
How much is x - 2y + 3z greater than 3x + 5y - 7?
Answer
Required expression:
= (x - 2y + 3z) - (3x + 5y - 7)
= x - 2y + 3z - 3x - 5y + 7
Collecting positive and negative like terms together, we get
x - 3x - 2y + 5y + 3z + 7
= -2x - 7y + 3z + 7
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Question 73 Marks
Simplify the following algebraic expressions by removing grouping symbols:
a - [2b - {3a - (2b - 3c)}]
Answer
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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Question 83 Marks
Simplify the following algebraic expressions by removing grouping symbols:
$20-\left[5 x y+3\left\{x^2-(x y-y)-(x-y)\right\}\right]$
Answer
First we have to remove the small brackets, or parentheses, (), then the curly brackets, \{\}, and then the square brackets,[].
Therefore, we have
$20-\left[5 x y+3\left\{x^2-(x y-y)-(x-y)\right\}\right]$
$=20-\left[5 x y+3\left\{x^2-x y+y-x+y\right\}\right]$
$=20-\left[5 x y+3\left\{x^2-x y+2 y-x\right\}\right]$
$=20-\left[5 x y+3 x^2-3 x y+6 y-3 x\right]$
$=20-\left[2 x y+3 x^2+6 y-3 x\right]$
$=20-2 x y-3 x^2-6 y+3 x$
$=-3 x^2-2 x y-6 y+3 x+20$
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Question 93 Marks
How much is $x^2-2 x y+3 y^2$ less than $2 x^2-3 y^2+x y$ ?
Answer
Required expression:
$=\left(2 x^2-3 y^2+x y\right)-\left(x^2-2 x y+3 y^2\right)$
$=2 x^2-3 y^2+x y-x^2+2 x y-3 y^2$
Collecting positive and negative like terms together, we get
$2 x^2-x^2-3 y^2-3 y^2+x y+2 x y$
$=x^2-6 y^2+3 x y$
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Question 103 Marks
Simplify the following algebraic expressions by removing grouping symbols:
-a - [a + {a + b - 2a - (a - 2b)} - b]
Answer
First we have to remove the small brackets, or parentheses, (), then the curly brackets, {}, and then the square brackets, [].
Therefore, we have
-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
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Question 113 Marks
Subtract:
$x^3+2 x^2 y+6 x y^2-y^3 \text { from } y^3-3 x y^2-4 x^2 y$
Answer
Required expression:
$=\left(y^3-3 x y^2-4 x^2 y\right)-\left(x^3+2 x^2 y+6 x y^2-y^3\right)$
$=y^3-3 x y^2-4 x^2 y-x^3-2 x^2 y-6 x y^2+y^3$
$=y^3+y^3-3 x y^2-6 x y^2-4 x^2 y-2 x^2 y-x^3$
$=2 y^3-9 x y^2-6 x^2 y-x^3$
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Question 123 Marks
Simplify the following algebraic expressions by removing grouping symbols:
85 - [12x - 7(8x - 3) - 2 {10x - 5(2 - 4x)}]
Answer
First we have to remove the small brackets, or parentheses, (), then the curly brackets, {}, and then the square brackets, [].
Therefore, we have
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
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Question 133 Marks
Simplify the following algebraic expressions by removing grouping symbols:
3x + 2y - [x - (2y - 3)]
Answer
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
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Question 143 Marks
Simplify the following algebraic expressions by removing grouping symbols:
5a - {3a - (2 - a) + 4}
Answer
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
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Question 153 Marks
Simplify the following algebraic expressions by removing grouping symbols:
$x^2-\left[3 x+\left\{2 x-\left(x^2-1\right)+2\right\}\right]$
Answer
First we have to remove the small brackets, or parentheses, (), then the curly brackets, \{\}, and then the square brackets, [].
Therefore, we have
$x^2-\left[3 x+\left\{2 x-\left(x^2-1\right)\right\}+2\right]$
$=x^2-\left[3 x+\left\{2 x-x^2+1\right\}+2\right]$
$=x^2-\left[3 x+2 x-x^2+1+2\right]$
$=x^2-\left[5 x-x^2+3\right]$
$=x^2-5 x+x^2-3$
$=2 x^2-5 x-3$
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Question 163 Marks
Simplify the following algebraic expressions by removing grouping symbols:
a - [b - {a - (b - 1) + 3a}]
Answer
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
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Question 173 Marks
What should be subtracted from $x^2-x y+y^2-x+y+3$ to obtain $-x^2+3 y^2-4 x y+1$ ?
Answer
LLet 'M' be the required expression. Then, we have
$x^2-x y+y^2-x+y+3-M$
$=-x^2+3 y^2-4 x y+1$
Therefore,
$M=\left(x^2-x y+y^2-x+y+3\right)-\left(-x^2+3 y^2-4 x y+1\right)$
$=x^2-x y+y^2-x+y+3+x^2-3 y^2+4 x y-1$
Collecting positive and negative like terms together, we get
$x^2+x^2-x y+4 x y+y^2-3 y^2-x+y+3-1$
$=2 x^2+3 x y-2 y^2-x+y+2$
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Question 183 Marks
Simplify the following algebraic expressions by removing grouping symbols:
$-2\left(x^2-y^2+x y\right)-3\left(x^2+y^2-x y\right)$
Answer
We have,
$-2\left(x^2-y^2+x y\right)-3\left(x^2+y^2-x y\right)$
Since the '-' sign precedes the parentheses, we have to change the sign of each term in the parentheses when we remove them.
$=-2 x^2+2 y^2-2 x y-3 x^2-3 y^2+3 x y$
$=-2 x^2-3 x^2+2 y^2-3 y^2-2 x y+3 x y$
$=-5 x^2-y^2+x y$
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Question 193 Marks
What should be added to xy - 3yz + 4zx to get 4xy - 3zx + 4yz + 7?
Answer
The required expression can be got by subtracting xy - 3yz + 4zx from 4xy - 3zx + 4yz + 7.
Therefore, required expression:
= (4xy - 3zx + 4yz + 7) - (xy - 3yz + 4zx)
= 4xy - 3zx + 4yz + 7 - xy + 3yz - 4zx
= 4xy - xy - 3zx - 4zx + 4yz + 3yz + 7
= 3xy - 7zx + 7yz + 7
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Question 203 Marks
Add $a^3+b^3-3$ to the sum of $2 a^3-3 b^3-3 a b+7$ and $-a^3+b^3+3 a b-9$.
Answer
First, we need to find the sum of $2 a^3-3 b^3-3 a b+7$ and $-a^3+b^3+3 a b-9$
$=\left(2 a^3-3 b^3-3 a b+7\right)+\left(-a^3+b^3+3 a b-9\right)$
Collecting positive and negative like terms together, we get
$=2 a^3-a^3-3 b^3+b^3-3 a b+3 a b+7-9$
$=a^3-2 b^3-2$
Now, the required expression:
$=\left(a^3+b^3-3\right)+\left(a^3-2 b^3-2\right)$
$=a^3+a^3+b^3-2 b^3-3-2$
$=2 a^3-b^3-5$
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Question 213 Marks
From,
$p^3-4+3 p^2$, take away $5 p^2-3 p^3+p-6$
Answer
Required expression:
$=\left(p^3-4+3 p^2\right)-\left(5 p^2-3 p^3+p-6\right)$
$=p^3-4+3 p^2-5 p^2+3 p^3-p+6$
$=p^3+3 p^3+3 p^2-5 p^2-p-4+6$
$=4 p^3-2 p^2-p+2$
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Question 223 Marks
Simplify the following algebraic expressions by removing grouping symbols:
2x - 3y - [3x - 2y - {x - z - (x - 2y)}]
Answer
First we have to remove the small brackets, or parentheses, (), then the curly brackets, {}, and then the square brackets, [].
Therefore, we have
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
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Question 233 Marks
Simplify the following algebraic expressions by removing grouping symbols:
85 - [12x - 7(8x - 3) - 2 {10x - 5(2 - 4x)}]
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Question 243 Marks
Add $x^2+2 x y+y^2$ to the sum of $x^2-3 y^2$ and $2 x^2-y^2+9$.
Answer
Sum of $x^2-3 y^2$ and $2 x^2-y^2+9$
$=\left(x^2-3 y^2\right)+\left(2 x^2-y^2+9\right)$
$=x^2+2 x^2-3 y^2-y^2+9$
$=3 x^2-4 y^2+9$
Now, required expression:
$=\left(x^2+2 x y+y^2\right)+\left(3 x^2-4 y^2+9\right)$
$=x^2+3 x^2+2 x y+y^2-4 y^2+9$
$=4 x^2+2 x y-3 y^2+9$
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Question 253 Marks
Simplify the following algebraic expressions by removing grouping symbols:
5 + [x - {2y - (6x + y - 4) + 2x} - {x - (y - 2)}]
Answer
First we have to remove the small brackets, or parentheses, (), then the curly brackets, {}, and then the square brackets, [].
Therefore, we have
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
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Question 263 Marks
Simplify the following algebraic expressions by removing grouping symbols:
-x + [5y - {2x - (3y - 5x)}]
Answer
First we have to remove the small brackets, or parentheses, (), then the curly brackets, {}, and then the square brackets, [].
Therefore, we have
-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
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Question 273 Marks
Subtract:
$-x^2-3 z \text { from } 5 x^2-y+z+7$
Answer
Required expression:
$=\left(5 x^2-y+z+7\right)-\left(-x^2-3 z\right)$
$=5 x^2-y+z+7+x^2+3 z$
$=5 x^2+x^2-y+z+3 z+7$
$=6 x^2-y+4 z+7$
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