Selina Concise Class 7 Math Chapter 11 Fundamental Concepts Exercise 11C Solution
EXERCISE 11C
(1) Multiply
(i) 3x ∗ 5x2y ∗ 2y
= (3 ∗ 5 ∗ 2) ∗ (x ∗ x2y ∗ y)
= 30x3y2
(ii) 5 ∗ 3a ∗ 2ab2
= (5 ∗ 3 ∗ 2) ∗ (a ∗ ab2)
= 30a2b2
(iii) 5x + 2y and 3xy
= (5x + 2y) ∗ 3xy
= 5x ∗ 3xy + 2y ∗ 3xy
=15x2y + 6xy2
(iv) (6a – 5b) ∗ (-2a)
= 6a ∗ (-2a) – 5b ∗ (-2a)
= -12a2 + 10ab
(v) (4a + 5b) (4a – 5b)
= 4a ∗ 4a + 5b ∗ 4a + 4a ∗ (-5b) + 5b ∗ (-5b)
= 16a2 + 20ab – 20ab – 25b2
= 16a2 – 25b2
(vi) 9xy + 2y2 and 2x – 3y
= (9xy + 2y2) x (2x – 3y)
= 9xy ∗ 2x + 2y2 ∗ 2x + 9xy ∗ (-3y) + 2y2 ∗ (-3y)
= 18x2y + 4xy2 – 27xy2 – 6y3
= 18x2y – 23 xy2 – 6y3
(vii) (-3m2n + 5mn – 4mn2) x 6m2n
= (-3m2n x 6m2n) + (5mn x 6m2n) – (4mn2 x 6m2n)
= -18m4n2 + 30m3n2 – 24m3n3
(viii) (6xy2 – 7x2y2 + 10x3) ∗ -3x2y3
= 6xy2 ∗ (-3x2y3) – 7x2y2 ∗ (-3x2y3) + 10x3 ∗ (-3x2y3)
= -18x3y5 + 21x4y5 – 30x5y3
(2) Copy and Complete the following multiplications:
(3) Evaluate
(i) (c + 5) (c -3)
= c ∗ c + 5 ∗ c + c ∗ (-3) + 5 ∗ (-3)
= c2 + 5c -3c – 15
= c2 +2c – 15
(ii) (3x – 5d) (4c – 6d)
= 3x ∗ 4c – 5d ∗ 4c + 3x ∗ (-6d) – 5d ∗ (-6d)
= 12cx – 20cd – 18dx +30d2
(iii) (1/2a + 1/2b) (1/2a – 1/2b)
= 1/2a x 1/2a + 1/2b x 1/2a + 1/2a x (- 1/2b) + 1/2b x (- 1/2b)
= ¼ a2 + ¼ ab – ¼ ab – ¼ b2
= ¼ a2 – ¼ b2
(iv) (a2 + 2ab + b2) (a + b)
= a2 x a + 2ab x a + b2 x a + a2 x b + 2ab x b + b2 x b
= a3 + 2a2b + ab2 + a2b + 2ab2 + b3
= a3 + 3 a2b + 3ab2 + b3
(v) (3x – 1) (4x3 – 2x2 + 6x – 3)
= 3x ∗ (4x3 – 2x2 + 6x – 3) – 1 ∗ (4x3 – 2x2 + 6x – 3)
= 12x4 – 6x3 + 18x2 – 9x – 4x3 + 2x2 – 6x + 3
= 12x4 – 10x3 + 20x2 – 15x + 3
(vi) (4m – 2) (m2 + 5m – 6)
= 4m x (m2 + 5m – 6) – 2 x (m2 + 5m – 6)
= 4m3+ 20m2 – 24m – 2m2 – 10m + 12
= 4m3 + 18m2 – 34m + 12
(vii) (8 – 12x + 7x2 – 6x3) (5 – 2x)
= 5 ∗ (8 – 12x + 7x2 – 6x3) – 2x ∗ (8 – 12x + 7x2 – 6x3)
= 40 – 60x + 35x2 – 30x3 – 16x + 24x2 – 14x3 + 12x4
= 40 – 76x + 59 x2 – 44 x3 + 12x4
(viii) (4x2 – 4x + 1) (2x3 – 3x2 + 2)
= 4x2 (2x3 – 3x2 + 2) – 4x (2x3 – 3x2 + 2) + 1 (2x3 – 3x2 + 2)
= 8x5 – 12x4 + 8x2 – 8x4 + 12x3 – 8x + 2x3 – 3x2 + 2
= 8x5 – 20x4 + 5x2 + 14x3 – 8x + 2
(ix) (6p2 – 8pq + 2q2) (-5p)
= -30p3– 40p2q – 10pq2
(x) – 4y (15x + 12y – 8z) (x – 2y)
= -60xy – 48y2 + 32yz ∗ (x – 2y)
= x ∗ (-60xy – 48y2 + 32yz) – 2y (-60xy – 48y2 + 32yz)
= -60x2y – 48xy2 + 32xyz + 120xy2 + 96y3 – 64y2z
= -60x2y + 72xy2 + 32xyz + 96y3 – 64y2z
(xi) (a2 + b2 + c2 – ab – bc – ca) (a + b + c)
= a x (a2 + b2 + c2 – ab – bc – ca) + b x (a2 + b2 + c2 – ab – bc – ca) + c (a2 + b2 + c2 – ab – bc – ca)
= a3 + ab2 + ac2 – a2b – abc – a2c + a2b + b3 + bc2 – ab2 – b2c – abc + a2c + b2c + c3 – abc – bc2 – ac2
= a3 – 3abc + b3 + c3
(4) Evaluate:
(i) (a + b) (a – b)
= a (a – b) + b (a – b)
= a2-ab+ab-b2
= a2 – b2
(ii) (a2 + b2) (a + b) (a – b)
= (a2 + b2) (a2 – b2)
= a4 – a2b2 + a2b2 – b4
= a4 – b4
(iii) (a4 + b4) (a2 + b2) (a + b) (a – b)
= (a4 + b4) (a2 + b2) (a2 – b2)
= (a4 + b4) (a4 – b4)
= a8 – b8
(5) Evaluate
(i) (3x – 2y) (4x + 3y)
= 3x (4x + 3y) – 2y (4x + 3y)
= 12x2 + 9xy – 8xy – 6y2
= 12x2 + 1xy – 6y2
(ii) (3x – 2y) (4x + 3y) (8x – 5y)
= (12x2 + 1xy – 6y2) (8x – 5y)
= 8x (12x2 + 1xy – 6y2) – 5y (12x2 + 1xy – 6y2)
= 96x3 + 8x2y – 48xy2 – 60x2y – 5xy2 + 30y3
= 96x3 – 52x2y – 53 xy2 + 30y3
(iii) (a + 5) (3a – 2) (5a + 1)
= {a x 3a + 5 x 3a + a x (-2) + 5 x (-2)} (5a + 1)
= {3a2 + 15a – 2a -10} (5a + 1)
= 3a2 + 13a – 10 (5a + 1)
= (3a2 + 13a – 10) x 5a + (3a2 + 13a – 10) x 1
= 15a3 + 65a2 – 50a + 3a2 + 13a – 10
= 15a3 + 68a2 – 37a – 10
(iv) (a+1) (a2 – a + 1) and (a – 1) (a2 + a + 1); and then (a + 1) (a2 – a + 1) + (a – 1) (a2 + a + 1)
(a+1) (a2 – a + 1) and (a – 1) (a2 + a + 1)
= a (a2 – a + 1) + 1 (a2 – a + 1) and a (a2 + a + 1) – 1 (a2 + a + 1)
= (a3 – a2 + a + a2 – a + 1) and (a3 + a2 + a – a2 – a – 1)
= (a3 + 1) and (a3 – 1)
Now, (a + 1) (a2 – a + 1) + (a – 1) (a2 + a + 1)
= (a3 + 1) + (a3 – 1) [From I]
= a3 + 1 + a3 – 1
= 2a3
(6) Multiply
(i) mn4 x m3n x 5m2n3
= 5m6n8
(ii) 2mnpq x 4mnpq x 5mnpq
= (2 x 4 x 5) (mnpq x mnpq x mnpq)
=40m2n2p2q2
(iii) pq – pm and p2m
= (pq – pm) x p2m
= p2m x pq – pm x p2m
= mp3q – m2p3
(iv) x3 – 3y3 and 4x2y2
= (x3 – 3y3) X (4x2y2)
= 4x5y2 – 3x2y5
(v) a3– 4ab and 2a2b
= (a3– 4ab) x 2a2b
= 2a5b – 8a3b2
(vi) x2 + 5yx – 3y2 and 2x2y
= (x2 + 5yx – 3y2) X 2x2y
= 2x4y + 10x3y2 – 6x2y3
(vi) x2 + 5yx – 3y2 and 2x2y
= (x2 + 5yx – 3y2) 2x2y
= 2x4y + 10x3y2 – 6x2y3
(7) Multiply:
(i) (2x + 3y) (2x + 3y)
= (2x + 3y)2 [as we know (a + b)2 = a2 + 2ab + b2]
= (2x)2 + 2 . 2x . 3y + (3y)2
= 4x2 + 12xy + 9y2
(ii) (2x – 3y) (2x + 3y)
= 2x (2x + 3y) – 3y (2x + 3y)
= 4x2 + 6xy – 6xy – 9y2
= 4x2 – 9y2
(iii) (2x + 3y) (2x – 3y)
= 2x (2x – 3y) + 3y (2x – 3y)
= 4x2 – 6xy + 6xy – 9y2
= 4x2 – 9y2
(iv) (2x – 3y) (2x – 3y)
= (2x – 3y)2
= (2x)2 – 2 . 2x . 3y + (3y)2
= 4x2 – 12xy + 9y2
(v) (-2x + 3y) (2x – 3y)
= -2x (2x – 3y) + 3y (2x – 3y)
= -4x2 + 6xy + 6xy – 9y2
= -4x2 – 9y2
(vi) (xy + 2b) (xy – 2b)
= (xy)2 – (2b)2
= x2y2 – 4b2
(vii) (x – a) (x + 3b)
= x (x + 3b) – a (x + 3b)
= x2 + 3bx – ax – 3ab
(viii) (2x + 5y + 6) (3x + y – 8)
= 2x (3x + y – 8) + 5y (3x + y – 8) + 6 (3x + y – 8)
= 6x2 + 2xy – 16x + 15xy + 5y2 – 40y + 18x + 6y – 48
= 6x2 + 17xy + 2x + 5y2 – 34y – 48
(ix) (3x – 5y + 2) (5x – 4y – 3)
= 3x (5x – 4y – 3) – 5y (5x – 4y – 3) + 2 (5x – 4y – 3)
= 15x2 – 12xy – 9x – 25xy + 20y2 + 15y + 10x – 8y – 6
= 15x2 – 37xy + 1x + 20y2 + 7y – 6
(x) (6x – 2y) (3x – y)
= {2 (3x – y)} (3x – y)
= 2 ∗ (3x – y) (3x – y)
= 2 * (3x – y)2
= 2 * (3x)2 – 2 . 3x . y + (y)2
= 2 * (9x2 – 6xy + y2)
= 18x2 – 12xy + 2y2
(xi) (1 + 6x2 – 4x3) (-1 + 3x – 3x2)
= 1 X (-1 + 3x – 3x2) + 6x2 X (-1 + 3x – 3x2) – 4x3 (-1 + 3x – 3x2)
= -1 + 3x – 3x2 – 6x2 + 18x3 – 18x4 + 4x3 – 12x4 + 12x5
= -1 + 3x – 9x2 + 22x3 – 30x4 + 12x5
Question 3-2nd answer is wrong the answer is 12c²-38cd – 30 d²
We will check it