Q1: Terms with same algebraic factors are called ____________ terms.
Ans: Like
Q2: A ________________ can take any value and ________________ has a fixed value.
Ans: variable , constant
Q3: An expression with one or more terms is called _____________
Ans: polynomial
Q4: An expression with one term is called __________________ with two terms is ______________ and with three terms is _______________
Ans: monomial ,binomial ,trinomial
Q5: An algebraic expression with equality sign is called ______________
Ans: equation
Q1: The degree of a constant term is 0
Ans: True
Q2: The sum or difference of two like terms may not like the given terms
Ans: False
Q3: 1 is an algebriac expression
Ans: True
Q4: The expression x + y + 5 x is a trinomial.
Ans: False
Q5: In like terms, the numerical coefficients should also be the same
Ans: False
Q1: The volume of a rectangular box where length, breadth, and height are 2a,4b,8c respectively.
Ans: Given: length of rectangular box, l=2a
Breadth of rectangular box, b=4b
Height of rectangular box, h=8c
We need to find the volume of the rectangular box with given dimensions.
We know, Volume of a cuboid =l×b×h
Therefore, the volume of the rectangular box will be
=2a×4b×8c=64abc
Q2: Simplify (p+q2)(p2−q)
Ans: Given: (p+q2)(p2−q)
We need to simplify the given expression.
To simplify, we will open the brackets by multiplying the terms in it with each other.
Therefore, the expression will become
(p+q2)(p2−q)
=p(p2−q)+q2(p2−q)
=p3−pq+q2p2−q3
Q3: If pq=3 and p+q=6, then (p2+q2) is
Ans: Given: pq=3
, p+q=6,
We need to find (p2+q2)
We know that,
(p+q)2=p2+q2+2pq
(p2+q2)=(p+q)2−2pq
Substituting the values, pq=3
, p+q=6,
in above equation we get
(p2+q2)=(6)2−2(3)=36−6=30
Q4: Simplify x(2x−1)+5 and find its value at x=−3
Ans: Given: x(2x−1)+5
We need to find the value of the given expression at x=−3
We will substitute x=−3 in the given expression.
Therefore, the expression after simplifying will be
2(−3)2−(−3)+5
=2(9)+3+5
=18+8
=26
Q5: Find the value of
Ans: Given:
We need to find the value of the given expression
We know that, (a−b)2=a2+b2−2ab
Therefore, using the formula, we will get the value of the expression as:
Q6: Think of a number x. Multiply it by 3 and add 5 to the product and subtract y subsequently. Find the resulting number.
Ans: Required number is (3x + 5)
Now we have to subtract y from the result i.e., 3x + 5 – y
Q7: From the sum of 3a−b+9 and −b−9, subtract 3a−b−9
Ans: Given: expressions 3a−b+9, −b−9, 3a−b−9
We need to subtract 3a−b−9
from the sum of 3a−b+9
and −b−9
The sum of the first two terms, −b−9
and 3a−b+9
will be
3a−b+9+(−b−9)=3a−b+9−b−9=3a−2b
Now subtracting 3a−b+9
from 3a−2b
, we get
3a−2b−(3a−b−9)=3a−2b−3a+b=9=−b+9
Q8: Find 194×206 using suitable identity
Ans: Given: 194×206
We need to find the value of the given expression using an identity.
We can write,194=(200−6)2
Using identity, (a−b)(a+b)=a2−b2, the given expression can be simplified as:
(200−6)(200+6)=(200)2−(6)2=40000−36=39964
Q9: If find the value of
Ans: Given:
To find:
Let
Square both sides, we will get
Now, we know that (a+b)2=a2+b2+2ab
So,
Q10: Simplify (x2−3x+2)(5x−2)−(3x2+4x−5)(2x−1)
Ans: Given: (x2−3x+2)(5x−2)−(3x2+4x−5)(2x−1)
We need to simplify the given expression.
First simplifying, (x2−3x+2)(5x−2),
we will get
(x2−3x+2)(5x−2)
=5x3−15x2+10x−2x2+6x−4
=5x3−17x2+16x−4 ...................(1)
Now simplifying, (3x2+4x−5)(2x−1), we will get
(3x2+4x−5)(2x−1)
=6x3+8x2−10x−3x2−4x+5
=6x3+5x2−14x+5 ..................(2)
Subtract (1)−(2) to get the result
(x2−3x+2)(5x−2)−(3x2+4x−5)(2x−1)
=5x3−17x2+16x−4−[6x3+5x2−14x+5]
=5x3−17x2+16x−4−6x3−5x2+14x−5
=−x3−22x2+30x−9
Q11: Find (3st+4t)2−(3st−4t)2
Ans: Given: (3st+4t)2−(3st−4t)2
We need to simplify the given expression.
We know that,
(a+b)2=a2+b2+2ab
∴(3st+4t)2=(3st)2+(4t)2+2(3st)(4t)
=9s2t2+16t2+24st2.................(1)
We also know that,
(a−b)2=a2+b2−2ab
∴(3st−4t)2=(3st)2+(4t)2−2(3st)(4t)(3st−4t)2
=9s2t2+16t2−24st2............(2)
Therefore, using equations (1) and (2) , the given expression will become
=9s2t2+16t2+24st2−[9s2t2+16t2−24st2]
=9s2t2+16t2+24st2−9s2t2−16t2+24st2=48st2
Q12: The area of a rectangle is uv where u is length and v is breadth. If the length of rectangle is increased by 5 units and breadth is decreased by 3 units. The new area of rectangle is?
Ans: Given: Area of the old rectangle =uv
Length of the old rectangle =u
Breadth of told rectangle =v
Length of the ew rectangle =u+5
Breadth of the new rectangle =v−3
We need to find the area of the new rectangle.
We know that, Area of rectangle =length×breadth
Therefore, the area of the new rectangle will be
=(u+5)(v−3)=uv−3u+5v−15
Q13: If =27, find
Ans: Given: =27
We need to find
Use identity, (a−b)2=a2+b2−2ab
Substitute, a=x, b= 1/x, we get
We know that, =27, therefore,
Q14: Simplify using identity,
Ans: Given: 0
We need to simplify the given expression using an identity.
Identity used:
1.a2−b2=(a+b)(a−b)2.(a−b)2=a2+b2−2ab
Using these identities, the given expression can be written as:
Q15: The sum of (x + 3) observations is (x4−81). Find the mean of the observations.
Ans: Given:
Number of observations =(x + 3)
Sum of observations =(x4−81)
We know that Mean=
Therefore, mean of the observations will be
We know that, a2−b2=(a+b)(a−b)
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1. What are algebraic expressions and how are they different from numerical expressions? |
2. Can you explain what an identity is in algebra? |
3. How do you simplify algebraic expressions? |
4. What is the importance of using identities in solving algebraic problems? |
5. How can I factor algebraic expressions, and why is it useful? |
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