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RD Chapter 4 Algebraic Identities Ex 4.3 Solutions

Question - 1 : - Find the cube of each of the following binomial expressions:

Answer - 1 : -


Question - 2 : - If a + b = 10 and ab = 21, find the value of a3 + b3.

Answer - 2 : -

a + b = 10, ab = 21
Cubing both sides,
(a + b)3 = (10)3
⇒ a3 +63 + 3ab (a + b) = 1000
⇒ a3 + b3 + 3 x 21 x 10 = 1000
⇒ a3 + b3 + 630 = 1000
⇒ a3 + b3 = 1000 – 630 = 370
∴ a3 +b3 = 370

Question - 3 : - If a – b = 4 and ab = 21, find the value of a3-b3.

Answer - 3 : -

a – b = 4, ab= 21
Cubing both sides,
⇒ (a –A)3 = (4)3
⇒ a3 –b3 – 3ab (a – b) = 64
⇒ a3-i3-3×21x4 = 64
⇒ a3 – 63 – 252 = 64
⇒ a3 – 63 = 64 + 252 =316
∴ a3 –b3 = 316

Question - 4 : -

Answer - 4 : -


Question - 5 : -

Answer - 5 : -


Question - 6 : -

Answer - 6 : -


Question - 7 : -

Answer - 7 : -


Question - 8 : -

Answer - 8 : -


Question - 9 : - If 2x + 3y = 13 and xy = 6, find the value of 8x3 + 21y3.

Answer - 9 : -

2x + 3y = 13, xy = 6
Cubing both sides,
(2x + 3y)3 = (13)3
⇒ (2x)3 +(3y)3 + 3 x 2x x 3X2x + 3y) = 2197
⇒ 8x3 +27y3 + 18xy(2x + 3y) = 2197
⇒ 8x3 +27y3 + 18 x 6 x 13 = 2197
⇒ 8X3 +27y3 + 1404 = 2197
⇒ 8x3 + 27y3 = 2197 – 1404 = 793
∴ 8x3 +27y3 = 793

Question - 10 : - If 3x – 2y= 11 and xy = 12, find the value of 27x3 – 8y3.

Answer - 10 : -

3x – 2y = 11 and xy = 12 Cubing both sides,
(3x – 2y)3 = (11)3
⇒ (3x)3 – (2y)3 – 3 x 3x x 2y(3x – 2y) =1331
⇒ 27x3 – 8y3 – 18xy(3x -2y) =1331
⇒  27x3 – 8y3 – 18 x 12 x 11 = 1331
⇒ 27x3 – 8y3 – 2376 = 1331
⇒ 27X3 – 8y3 = 1331 + 2376 = 3707
∴ 2x3 –8y3 = 3707

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