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Ncert Solutions for Algebraic Expressions and Identities Class 8 CBSE Part 4



In this page we have NCERT book Solutions for Class 8th Maths:Algebraic Expressions and Identities for EXERCISE 4 . Hope you like them and do not forget to like , social share and comment at the end of the page.

Question 1

 Multiply the binomials.

i) (2x + 5) and (4x – 3)

 (ii) (y – 8) and (3y – 4)

 (iii) (2.5l – 0.5m) and (2.5l + 0.5m)

 (iv) (a + 3b) and (x + 5)

 (v) (2pq + 3q2) and (3pq – 2q2)

 

Answer: 

Let  ( a+b) (c+d) to be done

then

( a+b) (c+d)= a(c+d) + b( c+d)

=a x  c+a x  d+b x  c+b x d

We will use the same concept in all the question below

 

i) (2x + 5)(4x - 3)

2x x 4x - 2x x 3 + 5 x 4x - 5 x 3

8x² - 6x + 20x -15

8x² + 14x -15

ii) ( y - 8)(3y - 4)

= y x 3y - 4y - 8 x 3y + 32

= 3y2 - 4y - 24y + 32

= 3y2 - 28y + 32

iii) (2.5l - 0.5m)(2.5l + 0.5)

Using (a+b)(a-b) = a2 - b2

We get = 6.25l2 - 0.25m2

iv) ax + 5a + 3bx + 15b

v) 2pq x 3pq - 2pq x 2q2 + 3q2 x 3pq - 3q2 x 2q2

= 6p2q2 - 4pq3 + 9pq3 - 6q4 

= 6p2q2 - 5pq3 - 6p4

 

Question 2

Find the product.

(i) (5 – 2x) (3 + x)

 (ii) (x + 7y) (7x – y)

iii) (a2+ b) (a + b2)

 (iv) (p2– q2) (2p + q)

 

Answer: 

i) 15 + 5x - 6x - 2x2

= 15 - x - x 2

ii) 7x2 - xy + 49xy - 7y2

= 7x2 - 7y2 + 48xy

iii) a2 x a + ax b + a x b + b3

= a3 + a2b + ab + b3

= a3 + b3 + a2b + ab

iv) 2p3 + p2q - 2pq2 - q3

= 2p3 - q3 + p2q - 2pq2

 

Question 3

 Simplify.

(i) (x2– 5) (x + 5) + 25

 (ii) (a2+ 5) (b3+ 3) + 5

 (iii) (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)

 (iv) (x + y)(2x + y) + (x + 2y)(x – y)

 (v) (x + y)(x2– xy + y2)

 (vi) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y

 (vii) (a + b + c)(a + b – c)

 

Answer:

i) x3 + 5x2 - 5x - 25 + 25

= x3 + 5x2 -5x

ii) a2b3 + 3a2 + 5b3 + 15 + 5

= a2b3 + 5b3 + 3a2 + 20

iii) (ac - ad + bc - bd) + (ac + ad - bc - bd) + (2ac + 2bd)

= ac - ad + bc - bd + ac + ad - bc - bd + 2ac + 2bd

= 4ac

iv) 2x2 + xy + 2xy + y2 + x2 - xy + 2xy - 2y2

= 3x2 + 4xy - y2

v) x3 - x2y + xy2 + x2y - xy2 + y3

= x3 + y3

vi) 2.25x2 + 6xy + 4.5x - 6xy - 16y2 - 12y - 4.5x + 12y

= 2.25x2 - 16y2

vii) a2 + ab - ac + ab + b2 - bc + ac + bc - c2

= a2 + b2 - c2 + 2ab

 

 

 

 

 


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