Question 13 Marks
Subtract: $6 x^3-7 x^2+5 x-3$ from $4-5 x+6 x^2-8 x^3$
AnswerRequired expression:
$=\left(4-5 x+6 x^2-8 x^3\right)-\left(6 x^3-7 x^2+5 x-3\right)$
$=4-5 x+6 x^2-8 x^3-6 x^3+7 x^2-5 x+3$
$=-8 x^3-6 x^3+7 x^2+6 x^2-5 x-5 x+3+4$
$=-14 x^3+13 x^2-10 x+7$
View full question & answer→Question 23 Marks
Simplify the following algebraic expressions by removing grouping symbols: $2a - [4b - {4a - 3(2a - b)}]$
AnswerFirst 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$
View full question & answer→Question 33 Marks
From, $x^3-5 x^2+3 x+1$, take away $6 x^2-4 x^3+5+3 x$
AnswerRequired expression:
$=\left(x^3-5 x^2+3 x+1\right)-\left(6 x^2-4 x^3+5+3 x\right)$
$=x^3-5 x^2+3 x+1-6 x^2+4 x^3-5-3 x$
$=x^3+4 x^3-5 x^2-6 x^2+1-5$
$=5 x^3-11 x^2-4$
View full question & answer→Question 43 Marks
From, $7+x-x^2$, take away $9+x+3 x^2+7 x^3$
AnswerRequired expression:
$=\left(7+x-x^2\right)-\left(9+x+3 x^2+7 x^3\right)$
$=7+x-x^2-9-x-3 x^2-7 x^3$
$=-7 x^3-x^2-3 x^2+7-9$
$=-7 x^3-4 x^2-2$
View full question & answer→Question 53 Marks
From, $1-5 y^2$, take away $y^3+7 y^2+y+1$
AnswerRequired expression:
$=\left(1-5 y^2\right)-\left(y^3+7 y^2+y+1\right)$
$=1-5 y^2-y^3-7 y^2-y-1$
$=-y^3-5 y^2-7 y^2-y$
$=-y^3-12 y^2-y$
View full question & answer→Question 63 Marks
How much is $x - 2y + 3z$ greater than $3x + 5y - 7$?
AnswerRequired expression: $= (x - 2y + 3z) - (3x + 5y - 7) = x - 2y + 3z - 3x - 5y + 7$
Collecting positive and negative like terms together,
we get $x - 3x - 2y + 5y + 3z + 7 = -2x - 7y + 3z + 7$
View full question & answer→Question 73 Marks
Simplify the following algebraic expressions by removing grouping symbols: $a - [2b - {3a - (2b - 3c)}]$
AnswerFirst 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 $
$= 4a - 4b + 3c$
View full question & answer→Question 83 Marks
Simplify the following algebraic expressions by removing grouping symbols:
$20-\left[5 x y+3\left\{x^2-(x y-y)-(x-y)\right\}\right]$
AnswerFirst we have to remove the small brackets, or parentheses, (), then the curly brackets, {}, and then the square brackets, []. Therefore, we have
$20-\left[5 x y+3\left\{x^2-(x y-y)-(x-y)\right\}\right]$
$=20-\left[5 x y+3\left\{x^2-x y+y-x+y\right\}\right]$
$=20-\left[5 x y+3\left\{x^2-x y+2 y-x\right\}\right]$
$=20-\left[5 x y+3 x^2-3 x y+6 y-3 x\right]$
$=20-\left[2 x y+3 x^2+6 y-3 x\right]$
$=20-2 x y-3 x^2-6 y+3 x$
$=-3 x^2-2 x y-6 y+3 x+20$
View full question & answer→Question 93 Marks
How much is $x^2-2 x y+3 y^2$ less than $2 x^2-3 y^2+x y$ ?
AnswerRequired 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
$2 x^2-x^2-3 y^2-3 y^2+x y+2 x y$
$=x^2-6 y^2+3 x y$
View full question & answer→Question 103 Marks
Simplify the following algebraic expressions by removing grouping symbols:
$-a - [a + {a + b - 2a - (a - 2b)} - b]$
AnswerFirst we have to remove the small brackets, or parentheses, $()$, then the curly brackets, ${}$, and then the square brackets, $[]$.
Therefore, we have
$-a - [a + {a + b - 2a - (a - 2b)} - b]$
$= -a - [a + {a + b - 2a - a + 2b} - b]$
$= -a - [a + {- 2a + 3b} - b]$
$= -a - [a - 2a + 3b - b]$
$= -a - [- a + 2b]$
$= -a + a - 2b$
$= -2b$
View full question & answer→Question 113 Marks
Subtract:
$x^3+2 x^2 y+6 x y^2-y^3$ from $y^3-3 x y^2-4 x^2 y$
AnswerRequired expression:
$=\left(y^3-3 x y^2-4 x^2 y\right)-\left(x^3+2 x^2 y+6 x y^2-y^3\right)$
$=y^3-3 x y^2-4 x^2 y-x^3-2 x^2 y-6 x y^2+y^3$
$=y^3+y^3-3 x y^2-6 x y^2-4 x^2 y-2 x^2 y-x^3$
$=2 y^3-9 x y^2-6 x^2 y-x^3$
View full question & answer→Question 123 Marks
Simplify the following algebraic expressions by removing grouping symbols: $85 - [12x - 7(8x - 3) - 2 {10x - 5(2 - 4x)}]$
AnswerFirst 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$
View full question & answer→Question 133 Marks
Simplify the following algebraic expressions by removing grouping symbols: $3x + 2y - [x - (2y - 3)]$
AnswerWe 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 $
$= 2x + 4y - 3$
View full question & answer→Question 143 Marks
Simplify the following algebraic expressions by removing grouping symbols: $5a - {3a - (2 - a) + 4}$
AnswerWe 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 $
$= 5a - 4a - 2 = a - 2$
View full question & answer→Question 153 Marks
Simplify the following algebraic expressions by removing grouping symbols:
$x^2-\left[3 x+\left\{2 x-\left(x^2-1\right)+2\right\}\right]$
AnswerFirst we have to remove the small brackets, or parentheses, $()$, then the curly brackets, {}, and then the square brackets, $[]$. Therefore, we have
$x^2-\left[3 x+\left\{2 x-\left(x^2-1\right)\right\}+2\right]$
$=x^2-\left[3 x+\left\{2 x-x^2+1\right\}+2\right]$
$=x^2-\left[3 x+2 x-x^2+1+2\right]$
$=x^2-\left[5 x-x^2+3\right]$
$=x^2-5 x+x^2-3$
$=2 x^2-5 x-3$
View full question & answer→Question 163 Marks
Simplify the following algebraic expressions by removing grouping symbols: $a - [b - {a - (b - 1) + 3a}]$
AnswerFirst 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 $
$= 5a - 2b + 1$
View full question & answer→Question 173 Marks
What should be subtracted from $x^2-x y+y^2-x+y+3$ to obtain $-x^2+3 y^2-4 x y+1$ ?
AnswerLet ' $M$ ' 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
$x^2+x^2-x y+4 x y+y^2-3 y^2-x+y+3-1$
$=2 x^2+3 x y-2 y^2-x+y+2$
View full question & answer→Question 183 Marks
Simplify the following algebraic expressions by removing grouping symbols:
$-2\left(x^2-y^2+x y\right)-3\left(x^2+y^2-x y\right)$
AnswerWe 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.
$=-2 x^2+2 y^2-2 x y-3 x^2-3 y^2+3 x y$
$=-2 x^2-3 x^2+2 y^2-3 y^2-2 x y+3 x y$
$=-5 x^2-y^2+x y$
View full question & answer→Question 193 Marks
What should be added to $xy - 3yz + 4zx$ to get $4xy - 3zx + 4yz + 7$?
AnswerThe 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 $
$= 3xy - 7zx + 7yz + 7$
View full question & answer→Question 203 Marks
Add $a^3+b^3-3$ to the sum of $2 a^3-3 b^3-3 a b+7$ and $-a^3+b^3+3 a b-9$.
AnswerFirst, 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:
$=\left(a^3+b^3-3\right)+\left(a^3-2 b^3-2\right)$
$=a^3+a^3+b^3-2 b^3-3-2$
$=2 a^3-b^3-5$
View full question & answer→Question 213 Marks
From, $p^3-4+3 p^2$, take away $5 p^2-3 p^3+p-6$
AnswerRequired expression:
$=\left(p^3-4+3 p^2\right)-\left(5 p^2-3 p^3+p-6\right)$
$=p^3-4+3 p^2-5 p^2+3 p^3-p+6$
$=p^3+3 p^3+3 p^2-5 p^2-p-4+6$
$=4 p^3-2 p^2-p+2$
View full question & answer→Question 223 Marks
Simplify the following algebraic expressions by removing grouping symbols: $2x - 3y - [3x - 2y - {x - z - (x - 2y)}]$
AnswerFirst 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 $
$= -x + y - z$
View full question & answer→Question 233 Marks
Simplify the following algebraic expressions by removing grouping symbols: $85 - [12x - 7(8x - 3) - 2 {10x - 5(2 - 4x)}]$
AnswerFirst 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 $
$= 44 + 104x$
View full question & answer→Question 243 Marks
Add $x^2+2 x y+y^2$ to the sum of $x^2-3 y^2$ and $2 x^2-y^2+9$.
AnswerSum 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:
$=\left(x^2+2 x y+y^2\right)+\left(3 x^2-4 y^2+9\right)$
$=x^2+3 x^2+2 x y+y^2-4 y^2+9$
$=4 x^2+2 x y-3 y^2+9$
View full question & answer→Question 253 Marks
Simplify the following algebraic expressions by removing grouping symbols: $5 + [x - {2y - (6x + y - 4) + 2x} - {x - (y - 2)}]$
AnswerFirst 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 $
$= 4x - 1$
View full question & answer→Question 263 Marks
Simplify the following algebraic expressions by removing grouping symbols: $-x + [5y - {2x - (3y - 5x)}]$
AnswerFirst 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 $
$= -8x + 8y$
View full question & answer→Question 273 Marks
Subtract:
$-x^2-3 z$ from $5 x^2-y+z+7$
AnswerRequired expression:
$=\left(5 x^2-y+z+7\right)-\left(-x^2-3 z\right)$
$=5 x^2-y+z+7+x^2+3 z$
$=5 x^2+x^2-y+z+3 z+7$
$=6 x^2-y+4 z+7$
View full question & answer→Question 283 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$x y-[y z-z x-\{y x-(3 y-x z)-(x y-z y)\}]$
View full question & answer→Question 293 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$85-[12 x-7(8 x-3)-2\{10 x-5(2-4 x)\}]$
View full question & answer→Question 303 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$-3 x^2-2 x y-6 y+3 x+20$
View full question & answer→Question 313 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$x^2-\left[3 x+\left\{2 x-\left(x^2-1\right)\right\}+2\right]$
View full question & answer→Question 323 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$5+[x-\{2 y-(6 x+y-4)+2 x\}-\{x-(y-2)\}]$
View full question & answer→Question 333 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$2 x-3 y-[3 x-2 y-\{x-z-(x-2 y)]$
View full question & answer→Question 343 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$-a-[a+\{a+b-2 a-(a-2 b)\}-b]$
View full question & answer→Question 353 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$2 a-[4 b-\{4 a-3(2 a-b)\}]$
View full question & answer→Question 363 Marks
Simplify the following algebraic expressions by removing grouping symbols.
$-x+[5 y-\{2 x-(3 y-5 x)]$
View full question & answer→Question 373 Marks
Add the following:
$4 a b-5 b c+7 c a$
$-3 a b+2 b c-3 c a$
$5 a b-3 b c+4 c a$
Answer$6 a b-6 b c+8 c a$
View full question & answer→Question 383 Marks
Add the following expressions:
$5 x^3+7+6 x-5 x^2, 2 x^2-8-9 x ; 4 x-2 x^2+3 x^3, 3 x^3-9 x-x^2$ and $x-x^2-x^3-4$
Answer$10 x^3-7 x^2-7 x-5$
View full question & answer→Question 393 Marks
Add the following expressions : $a^4-2 a^3 b+3 a b^3+4 a^2 b^2+3 b^4,-2 a^4-5 a b^3+7 a^3 b-6 a^2 b^2+b^4$
Answer$-a^4+5 a^3 b-2 a^2 b^2-2 a b^3+4 b^4$
View full question & answer→Question 403 Marks
Simplify each of the following: $12 a^2 b+3 b a^2$
View full question & answer→Question 413 Marks
Add the following:
$x-3 y-2 z$
$5 x+7 y-8 z$
$3 x-2 y+5 z$
View full question & answer→Question 423 Marks
Add the following expressions:
$8 a-6 a b+5 b,-6 a-a b-8 b$ and $-4 a+2 a b+3 b$
View full question & answer→Question 433 Marks
Add the following expressions:
$x^3-2 x^2 y+3 x y^2-y^3, 2 x^3-5 x y^2+3 x^2 y-4 y^3$
Answer$3 x^3+x^2 y-2 x y^2-5$
View full question & answer→Question 443 Marks
Simplify each of the following: $7 x^3 y+9 y x^3$
View full question & answer→Question 453 Marks
What must be added to $12 x^3-4 x^2+3 x-7$ to make the sum $x^3+2 x^2-3 x+2$ ?
Answer$-11 x^3+6 x^2-6 x+9$
View full question & answer→Question 463 Marks
From the sum of $3 x^2-5 x+2$ and $-5 x^2-8 x+9$ subtract $4 x^2-7 x+9$.
View full question & answer→Question 473 Marks
Identify the like terms and also mention the numerical coefficients of those terms:
$7 a^2 b c,-3 c a^2 b,-\frac{5}{2} a b c^2, \frac{3}{2} a b c^2,-\frac{4}{3} c b a^2$
AnswerLike terms :
$7 a^2 b c,-3 c a^2 b,-\frac{4}{3} c b a^2 ;-\frac{5}{2} a b c^2, \frac{3}{2} a b c^2$
Coefficients :$7,-3,-\frac{4}{3} ;-\frac{5}{2}, \frac{3}{2}$
View full question & answer→Question 483 Marks
Identify the like terms and also mention the numerical coefficients of those terms:
$4 x y,-5 x^2 y,-3 y x, 2 x y^2$
AnswerLike terms :$4 x y,-3 y x$
Coefficients :$4,-3$
View full question & answer→Question 493 Marks
Evaluate the following algebraic expressions for $x=1, y=-1, z=2, a=-2, b=1$, $c=-2$
$a x y+b y z+c x y$
View full question & answer→Question 503 Marks
Evaluate the following algebraic expressions for $x=1, y=-1, z=2, a=-2, b=1$, $c=-2$
$a x^2+b y^2-c z^2$
View full question & answer→