2 Mark Question

Question 12 Marks

Add the following:
$2 x^2 y,-4 x^2 y, 6 x^2 y,-5 x^2 y$

Answer

Adding the given terms,
We have,
$2 x^2 y+\left(-4 x^2 y\right)+\left(6 x^2 y\right)+\left(-5 x^2 y\right)$
$=2 x^2 y-4 x^2 y+6 x^2 y-5 x^2 y$
$=(2-4+6-5) x^2 y$
$=(8-9) x^2 y$
$=-x^2 y$

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Question 22 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

Required expression:
$=\left(5 x^3+7+6 x-5 x^2\right)+\left(2 x^2-8-9 x\right)+\left(4 x-2 x^2+3 x^3\right)+\left(3 x^3-9 x-x^2\right)+\left(x-x^2-x^3-4\right)$
Collecting positive and negative like terms together, we get
$5 x^3+3 x^3+3 x^3-x^3-5 x^2+2 x^2-2 x^2-x^2-x^2+6 x-9 x+4 x-9 x+x+7-8-4$
$=10 x^3-7 x^2-7 x-5$

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Question 32 Marks

Evaluate the following expressions for x = -2, y = -1, z = 3:
$\text{x}^2+\text{y}^2+\text{z}^2-\text{xy}-\text{yz}-\text{zx}$

Answer

$(-2)^2+\text{y}^2+\text{z}^2-\text{xy}-\text{yz}-\text{zx}$
$=(-2)^2+(-1)^2+(3)^2-(-2)(-1)-(-1)(3)-(3)(-2)$
$=4+1+9-2+3+6$
$=(4+1+9+3+6)-2$
$=23-2$
$=21$

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Question 42 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

Adding the given expressions,
We have,
$x^3-2 x^2 y+3 x y^2-y^3, 2 x^3-5 x y^2+3 x^2 y-4 y^3$
Collecting positive and negative like terms together, we get
$x^3+2 x^3-2 x^2 y+3 x^2 y+3 x y^2-5 x y^2-y^3-4 y^3$
$=3 x^3+x^2 y-2 x y^2-5 y^3$

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Question 52 Marks

Add the following:
7abc, -5abc, 9abc, -8abc

Answer

Adding the given terms,
We have,
7abc + (-5abc) + (9abc) + (-8abc)
= 7abc - 5abc + 9abc - 8abc
= (7 - 5 + 9 - 8)abc
= (16 - 13)abc
= 3abc

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Question 62 Marks

Simplify the following algebraic expressions by removing grouping symbols:
2x + (5x - 3y)

Answer

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

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Question 72 Marks

Add $2 x^2-3 x+1$ to the sum of $3 x^2-2 x$ and $3 x+7$.

Answer

Sum of $3 x^2-2 x$ and $3 x+7$
$=\left(3 x^2-2 x\right)+(3 x+7)$
$=3 x^2-2 x+3 x+7$
$=\left(3 x^2+x+7\right)$
Now, required expression:
$=2 x^2-3 x+1+\left(3 x^2+x+7\right)$
$=2 x^2+3 x^2-3 x+x+1+7$
$=5 x^2-2 x+8$

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Question 82 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

Adding the given expressions,
We have,
$a^4-2 a^3 b+3 a b^3+4 a^2 b^2+3 b^4,-2 a^4-5 a b^3+7 a^3 b-6 a^2 b^2+b^4$
$a^4-2 a^3 b+3 a b^3+4 a^2 b^2+3 b^4-2 a^4-5 a b^3+7 a^3 b-6 a^2 b^2+b^4$
Collecting positive and negative like terms together, we get
$a^4-2 a^4-2 a^3 b+7 a^3 b+3 a b^3-5 a b^3+4 a^2 b^2-6 a^2 b^2+3 b^4+b^4$
$=-a^4+5 a^3 b-2 a b^3-2 a^2 b^2+4 b^4$

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Question 92 Marks

Simplify the following algebraic expressions by removing grouping symbols:
3x - (y - 2x)

Answer

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

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Question 102 Marks

Add the following expressions:
8a - 6ab + 5b, -6a - ab - 8b and -4a + 2ab + 3b

Answer

Required expression:
= (8a - 6ab + 5b) + (-6a - ab - 8b) + (-4a + 2ab + 3b)
Collecting positive and negative like terms together, we get
8a - 6a - 4a - 6ab - ab + 2ab + 5b - 8b + 3b
= 8a - 10a - 7ab + 2ab + 8b - 8b
= -2a - 5ab

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Question 112 Marks

Identify the terms and also mention the numerical coefficients of those terms:
$\text{7a}^2\text{bc},-\text{3ca}^2\text{b},-\frac52\text{abc}^2,\frac32\text{abc}^2,-\frac43\text{cba}^2$

Answer

Like terms	Numerical coefficients
$\Big\{7\text{a}^2\text{bc},-\text{3ca}^2\text{b},-\frac43\text{cba}^2\Big\}\Big\{-\frac52\text{abc}^2,\frac{3}{2}\text{abc}^2\Big\}$	$\Big\{7,-3,-\frac43\Big\}\Big\{-\frac52,\frac32\Big\}$

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Question 122 Marks

Add the following:

x - 3y - 2z

5x + 7y - 8z

3x - 2y + 5z

Answer

Required expression:
= (x - 3y - 2z) + (5x + 7y - 8z) + (3x - 2y + 5z)
Collecting positive and negative like terms together, we get
x + 5x + 3x - 3y + 7y - 2y - 2z - 8z + 5z
= 9x - 5y + 7y - 10z + 5z
= 9x + 2y - 5z

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Question 132 Marks

Simplify the following algebraic expressions by removing grouping symbols:5a - (3b - 2a + 4c)

Answer

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

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Question 142 Marks

Add the following:

4ab - 5bc + 7ca

-3ab + 2bc - 3ca

5ab - 3bc + 4ca

Answer

Required expression:
= (4ab - 5bc + 7ca) + (-3ab + 2bc - 3ca) + (5ab - 3bc + 4ca)
Collecting positive and negative like terms together, we get
4ab - 3ab + 5ab - 5bc + 2bc - 3bc + 7ca - 3ca + 4ca
= 9ab - 3ab - 8bc + 2bc + 11ca - 3ca
= 6ab - 6bc + 8ca

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Maths 2 Mark Question

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