Question 12 Marks
Subtract:
$6 x^3-7 x^2+5 x-3 \text { from } 4-5 x+6 x^2-8 x^3$
Answer$ =4-5 x+6 x^2-8 x^3-\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 $
$ =7-10 x+13 x^2-14 x^3 $
$ =-14 x^3+13 x^2-10 x+7$
View full question & answer→Question 22 Marks
Subtract:
$-11 x^2 y^2+7 x y-6 \text { from } 9 x^2 y^2-6 x y+9$
Answer$-11 x^2 y^2+7 x y-6$ from $9 x^2 y^2-6 x y+9$
$ =9 x^2 y^2-6 x y+9-\left(-11 x^2 y^2+7 x y-6\right) $
$ =9 x^2 y^2-6 x y+9+11 x^2 y^2-7 x y+6 $
$ =20 x^2 y^2-13 x y+15 $
$ =15-13 x y+20 x^2 y^2 $
$ =20 x^2 y^2-13 x y+15$
View full question & answer→Question 32 Marks
If $p = -2, q = -1$ and $r = 3,$ find the value of: $p - q - r$
AnswerSubstituting $p = -2, q = -1$ and $r = 3$ in the given expression,
we get: $p - q - r = (-2) - (-1) - 3 = -2 + 1 - 3 = -4$
View full question & answer→Question 42 Marks
Add:
$x^3+y^3-z^3+3 x y z,-x^3+y^3+z^3-6 x y z, x^3-y^3-z^3-8 x y z$
Answer$x^3+y^3-z^3+3 x y z,-x^3+y^3+z^3-6 x y z, x^3-y^3-z^3-8 x y z$
$ =x^3+y^3-z^3+3 x y z+\left(-x^3\right)+y^3+z^3-6 x y z+x^3-y^3-z^3-8 x y z $
$ =\left(x^3-x^3+x^3\right)+\left(y^3+y^3-y^3\right)-\left(z^3-z^3+z^3\right)+(3 x y z-6 x y z-8 x y z) $
$ =x^3+y^3-z^3-11 x y z$
View full question & answer→Question 52 Marks
Simplify:
$2 p^3-3 p^2+4 p-5-6 p^3+2 p^2-8 p-2+6 p+8$
Answer$2 p^3-3 p^2+4 p-5-6 p^3+2 p^2-8 p-2+6 p+8$
$=2 p^3-6 p^3-3 p^2+2 p^2+4 p+6 p-5-2+8 $
$=-6 p^3-p^2+10 p+1$
View full question & answer→Question 62 Marks
If $p = -2, q = -1$ and $r = 3$, find the value of:
$3 p^2 q+5 p q^2+2 p q r$
AnswerSubstituting $p = -2, q = -1$ and $r = 3$ in the given expression, we get:
$3 p^2 q+5 p q^2+2 p q r$
$=3 \times(-2)^2 \times(-1)+5 \times(-2) \times(-1)^2+2 \times(-2) \times(-1) \times 3$
$= 3 \times 4 \times (-1) + 5 \times (-2) \times 1 + 12 = -12 - 10 + 12$
$= -10$
View full question & answer→Question 72 Marks
Add:
$2+x-x^2+6 x^3,-6-2 x+4 x^2-3 x^3, 2+x^2, 3-x^3+4 x-2 x^2$
Answer$2+x-x^2+6 x^3,-6-2 x+4 x^2-3 x^3, 2+x^2, 3-x^3+4 x-2 x^2 $
$ =2+x-x^2+6 x^3+(-6)-2 x+4 x^2-3 x^3+2+x^2+3-x^3+4 x-2 x^2$
$=(2-6+2+3)+(x-2 x+4 x)-\left(x^2-4 x^2-x^2+2 x^2\right)+\left(6 x^3-3 x^3-x^3\right)$
$ =1+3 x+2 x^2+2 x^3$
View full question & answer→Question 82 Marks
If $p = -2, q = -1$ and $r = 3$, find the value of:
$ p^2 + q^2 - r^2$
AnswerSubstituting $p = -2, q = -1$ and $r = 3$ in the given expression, we get:
$p^2+ q^2- r^2= (-2)^2+ (-1)^2- (3)^2$
$= 4 + 1 - 9$
$= 5 - 9 = -4$
View full question & answer→Question 92 Marks
Add:
$x^2-a^2,-5 x^2+2 a^2,-4 x^2+4 a^2$
Answer$x^2-a^2,-5 x^2+2 a^2,-4 x^2+4 a^2 $
$ =x^2-a^2+\left(-5 x^2\right)+2 a^2+\left(-4 x^2\right)+4 a^2 $
$ =x^2-a^2-5 x^2+2 a^2-4 x^2+4 a^2 $
$ =\left(x^2-5 x^2-4 x^2\right)-\left(a^2-2 a^2-4 a^2\right) $
$ =x^2-9 x^2-\left(a^2-6 a^2\right) $
$ =8 x^2-\left(-5 a^2\right) $
$ =-8 x^2+5 a^2=5 a^2-8 x^2$
View full question & answer→Question 102 Marks
If $p = -2, q = -1$ and $r = 3,$ find the value of:
$p^3+q^3+r^3+3 p q r$
AnswerSubstituting $p = -2, q = -1$ and $r = 3$ in the given expression, we get:
$p^3+q^3+r^3+3 p q r$
$=(-2)^3+(-1)^3+(3)^3+3 \times(-2) \times(-1) \times 3$
$= (-8) + (-1) + 27 + 18 = -8 - 1 + 27 + 18$
$= -9 + 45= 36$
View full question & answer→Question 112 Marks
Simplify: $4x - (3y - x + 2z)$
AnswerWe have:
$4x - (3y - x + 2z) $
$= 4x - 3y + x - 2z $
$= 4x + x - 2y - 2z $
$= 5x - 3y - 2z$
View full question & answer→Question 122 Marks
Add: $7xyz, -5xyz, 9xyz, -8xyz$
Answer$= 7xyz + (-5xyz) + 9xyz + (-8xyz)$
$= 7xyz - 5xyz + 9xyz - 8xyz$
$= (7xyz + 9xyz) - (5xyz + 8xyz)$
$= 16xyz - 13xyz = 3xyz$
View full question & answer→Question 132 Marks
Add:
$6 a^3,-4 a^3, 10 a^3,-8 a^3$
Answer$=6 a^3+\left(-4 a^3\right)+10 a^3+\left(-8 a^3\right)$
$ =\left(6 a^3+10 a^3\right)-\left(4 a^3+8 a^3\right)$
$ =16 a^3-12 a^3=4 a^3$
View full question & answer→Question 142 Marks
Add: $3a - 2b + 5c, 2a + 5b - 7c, - a - b + c$
Answer$3a - 2b + 5c, 2a + 5b - 7c, - a - b + c$
$ = 3a - 2b + 5c, 2a + 5b - 7c, -a - b + c $
$= (3a + 2a - a) - (2b - 5b + b) + (5c - 7c + c) $
$= 4a - (3b - 5b) + (6c - 7c) $
$= 4a + 2b - c$
View full question & answer→Question 152 Marks
Add: $2 x^3-3 x^2+7 x-8,-5 x^3+2 x^2-4 x+1,3-6 x+5 x^2-x^3 $
Answer$ 2 x^3-3 x^2+7 x-8,-5 x^3+2 x^2-4 x+1,3-6 x+5 x^2-x^3 $
$=2 x^3-3 x^2+7 x-8+\left(-5 x^3\right)+2 x^2-4 x+1+3-6 x+5 x^2-x^3 $
$ =\left(2 x^3-5 x^3-x^3\right)-\left(3 x^2-2 x^2-5 x^2\right)+(7 x-4 x-6 x)-(8-1-3) $
$ =\left(2 x^3-6 x^3\right)-\left(3 x^2-7 x^2\right)+(7 x-10 x)-(8-4) $
$ =-4 x^3+4 x^2-3 x-4$
View full question & answer→Question 162 Marks
Write the following using literals, numbers and signs of basic operations: One-third of $x$ multiplied by the sum of $a$ and $b$.
AnswerOne-third of $x$ is $\frac{\text{x}}{3}.$
The sum of $a$ and $b$ is $(a + b)$
$\therefore$ One third of $x$ multiplied by the sum of $a$ and $b$
$=\frac{\text{x}}{3}\times(\text{a + b})=\frac{\text{x}(\text{a + b})}{3}$
View full question & answer→Question 172 Marks
Add:
$2 x^2,-3 x^2, 7 x^2$
Answer$=2 x^2+\left(-3 x^2\right)+7 x^2 $
$ =9 x^2-3 x^2=6 x^2 $
View full question & answer→Question 182 Marks
How much less than $x - 2y + 3z$ is $2x - 4y - z$?
Answer$= (x - 2y + 3z) - (2x - 4y - z)$
$= x - 2y + 3z - 2x + 4y + z$
$= -x + 2y + 4z$
View full question & answer→Question 192 Marks
Subtract:$ -2a + b + 6d$ from $5a - 2b - 3c$
Answer$-2a + b + 6d$ from $5a - 2b - 3c $
$= 5a - 2b - 3c - (-2a + b + 6d)$
$ = 5a - 2b - 3c + 2a - b - 6d $
$= 7a - 3b - 3c - 6d$
View full question & answer→Question 202 Marks
If $x = 1, y = 2$ and $z = 5$, find the value of:
$2 x^2-3 y^2+z^2$
AnswerSubstituting $x = 1, y = 2$ and $z = 5$ in the given expression, we get:
$2 x^2-3 y^2+z^2=2 \times(1)^2-3 \times(2)^2+(5)^2$
$= 2 \times 1 - 3 \times 4 + 25$
$= 2 - 12 + 25$
$= 27 - 12 = 15$
View full question & answer→Question 212 Marks
If $x = 1, y = 2$ and $z = 5,$ find the value of: $3x – 2y + 4z$
AnswerSubstituting $x = 1, y = 2$ and $z = 5$ in the given expression,
we get: $3x - 2y + 4z $
$= 3 \times 1 - 2 \times 2 + 4 \times 5 $
$= 3 - 4 + 20 $
$= 23 - 4 $
$= 19$
View full question & answer→Question 222 Marks
If $x = 1, y = 2$ and $z = 5,$ find the value of:
$x^2+y^2+z^2$
AnswerSubstituting $x = 1, y = 2$ and $z = 5$ in the given expression, we get:
$x^2+y^2+z^2=(1)^2+(2)^2+(5)^2$
$= 1 + 4 + 25 = 30$
View full question & answer→Question 232 Marks
By how much does $1$ exceed $2x - 3y - 4$?
Answer$= 1 - (2x - 3y - 4)$
$= 1 - 2x + 3y + 4$
$= 5 - 2x + 3y$
View full question & answer→Question 242 Marks
By how much does $3 x^2-5 x+6 $ exceed $ x^3-x^2+4 x-1?$
Answer$=\left(3 x^2-5 x+6\right)-\left(x^3-x^2+4 x-1\right)$
$ =3 x^2-5 x+6-x^3+x^2-4 x+1$
$=-x^3+4 x^2-9 x+7$
View full question & answer→Question 252 Marks
What must be subtracted from $a^3- 4a^2+ 5a - 6$ to obtain $a^2- 2a + 1$?
Answer$=a^3-4 a^2+5 a-6-\left(a^2-2 a+1\right) $
$=a^3-4 a^2+5 a-6-a^2+2 a-1 $
$ =a^3-5 a^2+7 a-7 $
View full question & answer→Question 262 Marks
Simplify:
$x^4-6 x^3+2 x-7+7 x^3-x+5 x^2+2-x^4 $
Answer$x^4-6 x^3+2 x-7+7 x^3-x+5 x^2+2-x^4 $
$ =x^4-x^4-6 x^3+7 x^3+5 x^2+2 x-x-7+2 $
$ =x^3+5 x^2+x-5 $
View full question & answer→Question 272 Marks
Simplify:
$ 2 x^2-x y+6 x-4 y+5 x y-4 x+6 x^2+3 y $
Answer$ 2 x^2-x y+6 x-4 y+5 x y-4 x+6 x^2+3 y $
$ =2 x^2+6 x^2-x y+5 x y+6 x-4 x-4 y+3 y $
$ =8 x^2+4 x y+2 x-y $
View full question & answer→Question 282 Marks
Write the following using literals, numbers and signs of basic operations:
The product of $x$ and $y$ added to their sum.
AnswerThe product of $x$ and $y$ is $xy$
The sum of $x$ and $y$ is $(x + y)$
So, product of $x$ and $y$ added to their sum is $xy + (x + y)$
View full question & answer→Question 292 Marks
Subtract:
$x^3+2 x^2 y+6 x y^2-y^3$ from $y^3-3 x y^2-4 x^2 y$
Answer$x^3+2 x^2 y+6 x y^2-y^3$ from $ y^3-3 x y^2-4 x^2 y$
$ =y^3-3 x y^2-4 x^2 y-\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$
$ =2 y^3-9 x y^2-6 x^2 y-x^3 $
$ =-x^3+2 y^3-6 x^2 y-9 x y^2$
View full question & answer→Question 302 Marks
Subtract:
$5a + 7b - 2c$ from $3a - 7b + 4c$
Answer$5a + 7b - 2c$ from $3a - 7b + 4c$
$= (3a - 7b + 4c) - (5a + 7b - 2c)$
$= 3a - 7b + 4c - 5a - 7b + 2c$
$= -2a - 14b + 6c$
View full question & answer→Question 312 Marks
If $x = 1, y = 2$ and $z = 5$, find the value of:
$2 x^2 y-5 y z+x y^2 $
AnswerSubstituting $x = 1, y = 2$ and $z = 5$ in the given expression,
we get: $2 x^2 y-5 y z+x y^2 $
$ =2 \times(1)^2 \times 2-5 \times 2 \times 5+1 \times(2)^2$
$= 2 \times 1 \times 2 - 10 \times 5 + 1 \times 4$
$= 4 - 50 + 4$
$= 8 - 50 $
$= - 42$
View full question & answer→Question 322 Marks
Simplify:
$a - (b - 2a)$
AnswerWe have:
$a - (b - 2a)$
$= a - b + 2a$
$= a + 2a - b$
$= (1 + 2) a - b$
$= 3a - b$
View full question & answer→Question 332 Marks
By how much is $2x - 3y + 4z$ greater than $2x + 5y - 6z + 2$?
Answer$= (2x - 3y + 4z) - (2x + 5y - 6z + 2)$
$= 2x - 3y + 4z - 2x - 5y + 6z - 2$
$= -8y + 10z - 2$
View full question & answer→Question 342 Marks
If $x = 1, y = 2$ and $z = 5$, find the value of:$xy + yz - zx$
AnswerSubstituting $x = 1, y = 2$ and $z = 5$ in the given expression, we get:
$xy + yz - zx = 1 \times 2 + 2 \times 5 - 5 \times 1$
$= 2 + 10 - 5$
$= 12 - 5 = 7$
View full question & answer→Question 352 Marks
How much is $a + 2a - 3c$ greater than $2a - 3b + c$?
Answer$= (a + 2a - 3c) - (2a - 3b + c)$
$= a + 2a - 3c - 2a + 3b - c$
$= -a + 5b - 4$
View full question & answer→Question 362 Marks
Subtract: $a - 2b - 3c$ from $-2a + 5b - 4c$
Answer$a - 2b - 3c$ from $-2a + 5b - 4c$
$= -2a + 5b - 4c - (a - 2b - 3c) $
$= -2a + 5b - 4c - 4 + 2b + 3c$
$ = -3a + 7b - c$
View full question & answer→Question 372 Marks
Subtract:
$ 5 x^2-3 x y+y^2 $ from $ 7 x^2-2 x y-4 y^2 $
Answer$ 5 x^2-3 x y+y^2 $ from $7 x^2-2 x y-4 y^2 $
$ =7 x^2-2 x y-4 y^2-\left(5 x^2-3 x y+y^2\right)$
$ =7 x^2-2 x y-4 y^2-5 x^2+3 x y-y^2 $
$ =2 x^2+x y-5 y^2$
$ =2 x^2-5 y^2+x y $
View full question & answer→Question 382 Marks
If $p = -2, q = -1$ and $r = 3$, find the value of:
$p^4+ q^4- r^4$
AnswerSubstituting $p = -2, q = -1$ and $r = 3$ in the given expression, we get:
$p^4+q^4-r^4=(-2)^4+(-1)^4-(3)^4$
$= 16 + 1 - 81$
$= 17 - 81 = -64$
View full question & answer→Question 392 Marks
Add: $8a - 6ab + 5b, -6a - ab - 8b, -4a + 2ab + 3b$
Answer$8a - 6ab + 5b, -6a - ab - 8b, -4a + 2ab + 3b $
$= 8a - 6ab + 5b + (-6a) - ab - 8b + (-4a) + 2ab + 3b $
$= (8a - 6a - 4a) - (6ab + ab - 2ab) + (5b - 8b + 3ab)$
$ = -2a - (7ab - 2ab) + (8b - 8b) $
$= -2a - 5ab$
View full question & answer→Question 402 Marks
Add:$ 2 x^2-8 x y+7 y^2-8 x y^2, 2 x y^2+6 x y-y^2+3 x^2, 4 y^2-x y-x^2+x y^2 $
Answer$ 2 x^2-8 x y+7 y^2-8 x y^2, 2 x y^2+6 x y-y^2+3 x^2, 4 y^2-x y-x^2+x y^2 $
$ =2 x^2-8 x y+7 y^2-8 x y^2+2 x y^2+6 x y-y^2+3 x^2+4 y^2-x y-x^2+x y^2 $
$ =\left(2 x^2+3 x^2-x^2\right)-(8 x y-6 x y+x y)+\left(7 y^2-y^2+4 y^2\right)-\left(8 x y^2-2 x y^2-x y^2\right) $
$ =\left(5 x^2-x^2\right)-(9 x y-6 x y)+\left(11 y^2-y^2\right)-\left(8 x y^2-3 x y^2\right)$
$ =4 x^2-3 x y+10 y^2-5 x y^2 $
View full question & answer→Question 412 Marks
If $x = 1, y = 2$ and $z = 5$, find the value of:
$x^3– y^3– z^3$
AnswerSubstituting $x = 1, y = 2$ and $z = 5$ in the given expression, we get:
$x^3-y^3-z^3=(1)^3-(2)^3-(5)^3$
$= (1 \times 1 \times 1) - (2 \times 2 \times 2) - (5 \times 5 \times 5)$
$= 1 - 8 - 125$
$= 1 - 133$
$= - 132$
View full question & answer→Question 422 Marks
If $p = -2, q = -1$ and $r = 3,$ find the value of:
$ 2 p^2-q^2+3 r^2$
AnswerSubstituting $p = -2, q = -1$ and $r = 3$ in the given expression, we get:
$ 2 p^2-q^2+3 r^2$
$ =2 \times(-2)^2-(-1)^2+3 \times(3)^2 $
$= 2 \times 4 - 1 + 3 \times 9$
$= 8 - 1 + 27 = 34$
View full question & answer→