Mathematics Semester ii Solutions Solutions for Class 7 Math Chapter 5 Multiplication Of Algebraic Expressions are provided here with simple stepbystep explanations. These solutions for Multiplication Of Algebraic Expressions are extremely popular among class 7 students for Math Multiplication Of Algebraic Expressions Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Mathematics Semester ii Solutions Book of class 7 Math Chapter 5 are provided here for you for free. You will also love the adfree experience on Meritnation’s Mathematics Semester ii Solutions Solutions. All Mathematics Semester ii Solutions Solutions for class 7 Math are prepared by experts and are 100% accurate.
Page No 69:
Question O2:
How do we represent a ‘Universal set’ through Venn diagram.
Answer:
A universal set is represented by a rectangle.
Page No 75:
Question O1:
What is the expansion of (x + a) (x + b)
Answer:
The expansion of.
Page No 75:
Question O2:
Express 12 × 14 in the form of (x + a) (x + b)
Answer:
The term can be expressed in the form of as .
Page No 75:
Question O3:
Name the constant in the product of (m^{2} + 4) (m^{2} + 5)
Answer:
In, we have. Thus, the constant in the product of these is.
Page No 76:
Question W1:
Find the product using the formula.
Answer:
(1) (x + 3) (x + 7)
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + ab:
(x + 3) (x + 7) = x^{2} + (3 + 7) x + 21
= x^{2} + 10 x + 21
(2) (y + 3) (y + 5)
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + a b:
(y + 3) (y + 5) = y^{2} + (3 + 5) x + 15
= y^{2} + 8 y + 15
(3) (m + 4) (m + 5)
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + a b:
(m + 4) (m + 5) = m^{2} + (4 + 5) m + 20
= m^{2} + 9 m + 20
(4) (a + 10) (a + 5)
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + a b:
(a + 10) (a + 5) = a^{2} + (10 + 5) a + 20
= m^{2} + 15 m + 20
(5) (x + 8) (x + 2)
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + a b:
(x + 8) (x + 2) = x^{2} + (8 + 2) x + 16
= x^{2} + 10 x + 16
(6) (2a + 3) (2a − 7)
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + a b:
(2a + 3) (2a − 7) = 4a^{2} + (3 − 7) 2a − 21
= 4a^{2} − 8a − 21
(7) (2x − 5) (2x + 3)
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + a b:
(2x − 5) (2x + 3) = 4x^{2} + (−5 + 3) 2x − 15
= 4x^{2} − 4 x − 15
(8) (3x − 4) (3x + 8)
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + a b:
(3x − 4) (3x + 8) = (3x)^{2} + (−4 + 8) 3x + (−4) × 8
= 9x^{2} + 12 x − 32
(9) (a^{2} − 3) (a^{2} − 5)
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + ab:
(a^{2} − 3) (a^{2} − 5) = a^{4} + (−3 − 5) a^{2} + (−3) × (−5)
= a^{4} − 8a^{2} + 15
(10) (3p^{2} + 1) (3p^{2} + 4)
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + ab:
(3p^{2} + 1) (3p^{2} + 4) = (3p)^{4} + (1 + 4) 3p^{2} + 1 × 4
= 9p^{4} + 15p^{2} + 4
Page No 76:
Question W2:
Find the product of the following numbers using the formula (x + a) (x + b).
Answer:
(1) 105 × 108
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + ab;
105 × 108 = (100 + 5) (100 + 8)
= (100)^{2} + (5 + 8) × 100 + 5 × 8
= 10000 + 1300 + 40
= 11340
(2) 130 × 98
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + a b:
130 × 98 = (100 + 30) (100 − 2)
= 10000 + (30 − 2) × 100 + 30 × (−2)
= 10000 + 2800 − 60
= 12740
(3) 104 × 94
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + ab:
104 × 94 = (100 + 4) (100 − 6)
= 10000 + (4 − 6) × 100 + 4 × (−6)
= 10000 − 200 − 24
= 9776
(4) 99 × 97
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + a b:
99 × 97 = (100 − 1) (100 − 3)
= 10000 + (−1 − 3)×100 + 3
= 10000 − 400 + 3
= 9603
(5) 112 × 90
Using the identity (x + a) (x + b) = x^{2} + (a + b) x + a b:
112 × 90 = (100 + 12) (100 − 10)
= 10000 + (12 − 10) × 100 + 12 × (−10)
= 10000 + 200 − 120
= 10080
Page No 80:
Question O1:
What is the expanded form of (a + b)^{2}
Answer:
The expanded form of is .
Page No 80:
Question W1:
Expand by using a suitable formula.
Answer:
(1) Using the identity (a + b)^{2} = a^{2} + 2ab + b^{2}:
(2) Using the identity (a + b)^{2} = a^{2} + 2ab + b^{2}:
(3) Using the identity (a + b)^{2} = a^{2} + 2ab + b^{2}:
(4) Using the identity (a + b)^{2} = a^{2} + 2ab + b^{2}:
(5) Using the identity (a + b)^{2} = a^{2} + 2ab + b^{2}:
(6) Using the identity (a + b)^{2} = a^{2} + 2ab + b^{2}:
(7) Using the identity (a + b)^{2} = a^{2} + 2ab + b^{2}:
(8) Using the identity (a + b)^{2} = a^{2} + 2ab + b^{2}:
(9) Using the identity (a + b)^{2} = a^{2} + 2ab + b^{2}:
(10) Using the identity (a + b)^{2} = a^{2} + 2ab + b^{2}:
Page No 80:
Question O2:
Express (12)^{2} in the form of (a + b)^{2}
Answer:
(12)^{2} can be expressed as .
Page No 80:
Question W2:
Find the squares of the following numbers using the formula.
(a + b)^{2} = a^{2} + 2ab + b^{2}
Answer:
(1)
(2)
(3)
(4)
(5)
Page No 80:
Question W3.2:
The length of each side of a square land shown in the figure is (a + b) units. In the corner of this land there is a square portion of length ‘b’ units is useless. Find the area of the portion of the land which is useful.
Answer:
Total area of the square land = (a + b)^{2} = a^{2} + 2ab + b^{2}
Area of useless land = b^{2}
∴ Useful land = a^{2} + 2ab + b^{2} − b^{2} = (a^{2} + 2ab) sq units
Page No 80:
Question W3.1:
Find the area of a square having its side (3x + 2y) using the formula.
Answer:
Side = 3 x + 2 y
Using the identity (a + b)^{2} = a^{2} + 2ab + b^{2}:
Page No 80:
Question O3:
Expand (m + 2)^{2}
Answer:
=
Page No 80:
Question W4.1:
Fill up the blanks.
Answer:
Page No 80:
Question W4.2:
Fill up the blanks.
Answer:
Page No 80:
Question W4.3:
Fill up the blanks.
Answer:
Page No 83:
Question W1:
Use the formula and expand the following:
Answer:
(1) Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
(2) Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
(3) Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
(4) Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
(5) Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
(6) Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
(7) Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
(8) Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
(9) Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
(10) Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
Page No 83:
Question O1:
Expand (a − b)^{2}
Answer:
The expansion of .
Page No 83:
Question O2:
Express (8)^{2} in the form of (a − b)^{2}
Answer:
(8)^{2 }can be expressed in the form of , as .
Page No 83:
Question W2:
Find the square of the following numbers using the formula:
(a − b)^{2} = a^{2} − 2ab + b^{2}
Answer:
(1)
(2)
(3)
(4)
(5)
Page No 83:
Question O3:
Expand (p − 3)^{2}
Answer:
The expansion of is .
Page No 84:
Question W3.1:
Fill in the blanks with appropriate answers:
Answer:
Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
Page No 84:
Question W3.2:
Fill in the blanks with appropriate answers:
Answer:
Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
Page No 84:
Question W3.3:
Fill in the blanks with appropriate answers:
Answer:
Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
_{Therefore, the missing terms are 24}_{ab}_{, 4}_{a}_{ and 3}_{b}
Page No 84:
Question W3.4:
Fill in the blanks with appropriate answers:
Answer:
Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
Page No 84:
Question W3.5:
Fill in the blanks with appropriate answers:
Answer:
Using the identity (a − b)^{2} = a^{2} − 2ab + b^{2}:
Page No 86:
Question O1:
What is the expanded form of (a + b) (a − b).
Answer:
The expanded form of is .
Page No 86:
Question O2:
Find the product of (p + 4) (p − 4).
Answer:
Page No 86:
Question O3:
Expand 12 × 8 by using the formula (a + b) (a − b).
Answer:
Page No 87:
Question W1:
Use the formula and find the product:
1) 
2) 

3) 
4) 

5) 
6) 

7) 
8) 

9) 

10) 
Answer:
(1) Using the identity (a + b) (a − b) = a^{2} − b^{2}:
(2) Using the identity (a + b) (a − b) = a^{2} − b^{2}:
(3) Using the identity (a + b) (a − b) = a^{2} − b^{2}:
(4) Using the identity (a + b) (a − b) = a^{2} − b^{2}:
(5) Using the identity (a + b) (a − b) = a^{2} − b^{2}:
(6) Using the identity (a + b) (a − b) = a^{2} − b^{2};
(7) Using the identity (a + b) (a − b) = a^{2} − b^{2}:
(8) Using the identity (a + b) (a − b) = a^{2} − b^{2}:
(9) Using the identity (a + b) (a − b) = a^{2} − b^{2}:
(10) Using the identity (a + b) (a − b) = a^{2} − b^{2}:
Page No 87:
Question W2:
Use the formula and find the product:
Answer:
(1) Using the identity (a + b) (a − b) = a^{2} − b^{2}:
(2) Using the identity (a + b) (a − b) = a^{2} − b^{2}:
(3) Using the identity (a + b) (a − b) = a^{2} − b^{2}:
Page No 87:
Question W3:
Match the following:
A 
B 

1) 
(m + 2n) (m − 2n) 
a) 
m^{2} − 16 
2) 
(3m + n) (3m − n) 
b) 
4m^{2} − 25n^{2} 
3) 
(m + 4) (m − 4) 
c) 
4m^{2} + 25n^{2} 
4) 
(2m + 5n) (2m − 5n) 
d) 
m^{2} − 4n^{2} 

e) 
9m^{2} + n^{2} 


f) 
9m^{2} − n^{2} 
Answer:
Using the identity (a + b) (a − b) = a^{2} − b^{2}:
(1)
(2)
(3)
(4)
_{Hence, the match is (1) − (}_{d}_{), (2) − (}_{f}_{), (3) − (}_{a}_{) and (4) − (}_{b}_{)}
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