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Published on: 31/10/2025
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Questions + Answers key
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1.
Simplify these expressions and find their values, if x = 3, a = - 1, b = - 2.
10- 3b- 4- 5b
2.
Subtract the following expressions:- a2- ab from b2 + ab
3.
Write the like terms in the expression
4x2 yz + 7xy2z - 14xyz + 7x2yz2 + 14xyx2 - 15xy2z+ 10zxy2 +13y2 xz
4.
Find the sum of x - y and x + y.
5.
Describe how the following expressions are obtained? x2y
6.
Simplify the expression and find their value at p = 3, x = -1, Y = - 2
2x - 2y - 4 - 5 + P
7.
Simplify: 14x - [7x3 + 3x2 - {8x2 - (4 - x - x3) - 6x3} - 2x3].
8.
State whether each pair of terms given below is like or unlike 3x2y and 5xy2
9.
Observe the patterns of digits made from line segments of equal length. You will find such segmented digits on the display of electronic watches or calculators.

10.
From the sum of 3x- y+ 11 and -y- 11, subtract 3x- y- 11.
11.
Rohan's mother gave him Rs 3xy2 and his father gave him Rs5(xy2 + 2). Out of this total money, he spent Rs(10 - 3xy2) on his birthday party. How much money is left with him? Which value is depicted here?
12.
What should be added to 3pq +5p2q2 + p3 to get p3 + 2p2q2?
13.
The value of 3x2 - 5x + 3 when x = 1 is
1
0
-1
11
14.
- b - 0 is equal to
-1xb
1 -b - 0
0 - (-1) x b
-b - 0 - 1
15.
The algebraic language of "Twice the cube of a number x subtracted from five times the sum of y and 2" is
5y + 2 - 2x3
2x3 - 5y + 2
5(y+2)-2x3
5(y+2)-(2x)3
16.
The degree of the polynomial 5x3 - 2x2 + 1 is
3
2
0
4
17.
Number of terms in the expression 3x2 y - 2y2z-z2x + 5 is
2
3
4
5
18.
When we subtract a monomial from a trinomial, then answer can be a polynomial.
19.
\(1+{x\over2}+x^3\) is a polynomial.
20.
The sum of 4x2 with - 8x2 is 4x2.
21.
If (x2y + y2 + 3) is subtracted from (3x2y + 2y2 + 5),then coefficient of y in the result is...............
22.
The speed of car is 55 km/h The distance covered in y h is
23.
The sum of 2xy - 6xy2 and 3xy + 5xy2 is.............
24.
In x4, 4 is called the..............
25.
3a2b and - 7 ba2 are......terms
26.
If a = 1, b = 1 then 6a2 - 2ab - 2b2 is
27.
[13a - 2ab -2 (a+ b)]
28.
The sum of -2x2y2 and -9x2y2
29.
The sum of 9x2y2 and 2x2 y2 is
1.
The simplified expression is 6 - 8b and its required value is 22.
2.
a2 + b2 + 2ab
3.
The like terms are 7xy2z,- 15xy2z, 10zxy2,13y2xz
4.
Given, algebraic expressions are (x - y) and (x + y).
By horizontal method, x - y + x + Y = x + x - y + Y = 2x
By column method,
x - y
+x + y
______
2x + 0 or 2x
_______
5.
In x2 y, first obtain x2 by multiplying the variable x by itself and then multiply x2 by y to get the expression x2y
6.
-4
7.
-10x3+5x2+15x-4
8.
Given, 3x2y and 5xy2
Here, 3x2y and 5xy2 is unlike pair.
9.
Given, the algebraic expression which give the number of segments required to form n digits of Y is (3n + 1).
If n = 5, then 3n + 1= 3 x 5 + 1= 15 + 1= 16 So, 16 segments are required to form 5 digits of 4.
If n = 10, then 3n + 1= 3 x 10 + 1= 30 + 1= 31 So, 31 segments are required to form 10 digits of 4.
If n = 100, then 3n + 1= 3 x 100 + 1= 300 + 1= 301 So, 301 segments are required to form 100 digits of 4.
10.
We first find the sum of 3x - y + 11 and -y - 11
\(3xy-y+11\\\quad\ \ -y-11\\ \_\_\_\_\_\_\_\_\_\_\_\\\quad 3x-2y\\\_\_\_\_\_\_\_\_\_\_\_\)
Now, we have to subtract 3x - y - 11 from the sum 3x - 2y
\(3x-2y\\3x-y-11\\-\ +\ \ \ +\\ \_\_\_\_\_\_\_\_\_\_\_\\0-y\ \ \ \ +11\\\_\_\_\_\_\_\_\_\_\_\_\)
Hence, the Required answer - y + 11
11.
Given, amount given to Rohan by his mother = Rs 3xy2
Amount given to Rohan by his father = Rs 5( xy2 + 2)
Total amount spent by Rohan =Rs 10 - 3xy2
:. Money left with Rohan
= 3xy2 + 5(xy2 + 2) - (10 - 3xy2)
= 3xy2 + 5xy2 + 10 -10 + 3xy2
= 3xy2 + 5xy2 + 3xy2 + 10 -10 = Rs.11 xy2
12.
Required expression is
p3 + 2p2q2 -(3pq + 5p2q2 + p3)
= p3 + 2p2q2 - 3pq _ 5p2q2 - p3
= p3 -p3 + 2p2q2 _ 5p2q2 - 3pq
= - 3p2q2 - 3pq
So, if we add - 3p2q2 - 3pq in
3pq + 5p2q2 + p3, we get p3 + 2p2q2.
13.
(a)
1
14.
(a)
-1xb
15.
(c)
5(y+2)-2x3
16.
(a)
3
17.
(c)
4
18.
(a)
19.
(a)
20.
(b)
21.
( )
2x2
22.
( )
55y km
23.
Sum of 2xy - 6xy2 and 3xy +5xy2
= 2xy - 6xy2 +3xy +5xy2 = 5xy -6xy2 +5xy2
= 5xy - xy2
The sum of 2xy - 6xy2 and 3xy +5xy - 6xy2 + 5xy2
24.
( )
exponent
25.
( )
like
26.
( )
2
27.
( )
11a-2b-2ab
28.
( )
-11x2y2
29.
( )
11x2y2
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