The Total solution for NCERT class 6-12
(v) (2pq + 3q2)and (3pq – 2q2)
(vi) (3/4 a2 +3b2) and4( a2 –2/3 b2)
Answer - 1 : -
(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 +0.5m)
= 2.5l x 2.5 l + 2.5l x 0.5m – 0.5m x 2.5l –0.5m x 0.5m
=6.25l2 + 1.25 lm – 1.25 lm – 0.25 m2
=6.25l2– 0.25 m2
iv) (a + 3b) (x + 5)
=ax + 5a + 3bx + 15b
(v) (2pq + 3q2) (3pq – 2q2)
= 2pq x 3pq – 2pq x 2q2 + 3q2 x 3pq – 3q2 x 2q2
= 6p2q2 – 4pq3 + 9pq3 – 6q4
= 6p2q2 + 5pq3 – 6q4
(vi) (3/4 a² + 3b² ) and 4( a² – 2/3 b² )
=(3/4 a² + 3b² ) x 4( a² – 2/3 b² )
=(3/4 a² + 3b² ) x (4a² – 8/3 b² )
=3/4 a² x (4a² – 8/3 b² ) + 3b² x (4a² – 8/3 b² )
=3/4 a² x 4a² -3/4 a² x 8/3 b² + 3b² x 4a² – 3b² x 8/3 b²
=3a4 – 2a² b² + 12 a² b² – 8b4
= 3a4 + 10a² b² – 8b4
Answer - 2 : -
(i) (5 – 2x) (3 + x)
= 5 (3 + x) – 2x (3 + x)
=15 + 5x – 6x – 2x2
= 15 – x -2 x 2
(ii) (x + 7y) (7x – y)
= x(7x-y) + 7y ( 7x-y)
=7x2 –xy + 49xy – 7y2
= 7x2 –7y2 +48xy
iii) (a2+ b) (a+ b2)
= a2 (a + b2) + b(a+ b2)
= a3 + a2b2 +ab + b3
= a3 + b3 + a2b2 + ab
iv) (p2– q2) (2p + q)
= p2 (2p + q)– q2 (2p+ q)
=2p3 + p2q – 2pq2 – q3
= 2p3 – q3 + p2q – 2pq2
Simplify.
(i) (x2– 5) (x+ 5) + 25
(ii) (a2+ 5) (b3+ 3) + 5
(iii)(t + s2)(t2 – s)
(iv) (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)
(v) (x + y)(2x + y) + (x + 2y)(x – y)
(vi) (x + y)(x2– xy + y2)
(vii) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y
(viii) (a + b + c)(a + b – c)
Answer - 3 : -
i) (x2– 5) (x+ 5) + 25
= x3 +5x2 –5x – 25 + 25
= x3 +5x2 –5x
ii) (a2+ 5) (b3+ 3) + 5
= a2b3 + 3a2 +5b3 +15 + 5
= a2b3 + 5b3 +3a2 +20
iii) (t + s2)(t2 – s)
= t (t2 – s) + s2(t2 –s)
= t3 – st + s2t2 – s3
= t3 – s3 – st + s2t2
iv) (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)
= (a + b) (c – d) + (a – b) (c + d) + 2 (ac + bd)
=(ac – ad + bc – bd) + (ac + ad – bc – bd) + (2ac + 2bd)
= ac – ad + bc – bd + ac + ad – bc – bd + 2ac + 2bd
= 4ac
v) (x + y)(2x + y) + (x + 2y)(x – y)
= 2x2 +xy + 2xy + y2 + x2 – xy + 2xy – 2y2
= 3x2 +4xy – y2
vi) (x + y)(x2– xy + y2)
= x3 – x2y + xy2 + x2y – xy2 + y3
= x3 + y3
vii) (1.5x – 4y)(1.5x + 4y + 3) – 4.5x + 12y
= 2.25x2 +6xy + 4.5x – 6xy – 16y2 –12y – 4.5x + 12y = 2.25x2 –16y2
viii) (a + b + c)(a + b – c)
= a2 +ab – ac + ab + b2 –bc + ac + bc – c2
= a2 + b2 – c2 +2ab