POLYNOMIALS 2282021 1 POLYNOMIALS Factorise 1 4 x

POLYNOMIALS Factorise 1) 4 x 2 + 9 y 2 + 16 z 2

POLYNOMIALS Write the following cubes in expanded form. 1) (2 x + 1)3 Sol:

POLYNOMIALS 2) (2 a – 3 b)3 Sol: It is in the form of

POLYNOMIALS Evaluate: 1) ( 99 )3 Sol: ( 99)3 = ( 100 – 1

POLYNOMIALS Factorise: 1) 8 a 3 + b 3 + 12 a 2 b

Slides: 6

Download presentation

POLYNOMIALS 2/28/2021 1

POLYNOMIALS Factorise 1) 4 x 2 + 9 y 2 + 16 z 2 + 12 xy – 24 yz – 16 xz Sol: Consider 4 x 2 + 9 y 2 + 16 z 2 + 12 xy – 24 yz – 16 xz = (2 x)2 + (3 y)2 + (-4 z)2 + 2(2 x)(3 y) + 2(3 y)(-4 z) + 2(2 x)(-4 z) = (2 x + 3 y – 4 z)2 [(a + b + c)2 = a 2 + b 2 + c 2 + 2 ab + 2 bc + 2 ca Here a = 2 x, b = 3 y &c = -4 z] 2/28/2021 2

POLYNOMIALS Write the following cubes in expanded form. 1) (2 x + 1)3 Sol: It is the form (a + b)3 = a 3 + b 3 + 3 ab(a + b) Here a = 2 x, b = 1 ∴(2 x + 1)3 = (2 x)3 + 13 + 3(2 x)(1) (2 x + 1) = 8 x 3 + 12 x 2 + 6 x + 1 2/28/2021 3

POLYNOMIALS 2) (2 a – 3 b)3 Sol: It is in the form of (a – b)3 = a 3 – b 3 – 3 ab (a – b) ∴ (2 a – 3 b)3 = (2 a)3 – (3 b)3 – 3(2 a)(3 b) [2 a – 3 b] = 8 a 3 – 27 b 3 – 36 a 2 b + 54 ab 2 2/28/2021 4

POLYNOMIALS Evaluate: 1) ( 99 )3 Sol: ( 99)3 = ( 100 – 1 )3 It is in the form of ( a – b )3 ( 100 – 1 )3 = ( 100 )3 – 3 (100× 1 ) (100 – 1 ) – (1)3 = 1000000 – 300 ( 100 – 1 ) – 1 = 1000000 – 30000 + 300 – 1 = 970299 2/28/2021 5

POLYNOMIALS Factorise: 1) 8 a 3 + b 3 + 12 a 2 b + 6 ab 3 Sol: It is in the form of a 3 + b 3 + 3 ab (a + b )=(a + b)3 Here a = 2 a , b = b 8 a 3 + b 3 + 12 a 2 b + 6 ab 3 = ( 2 a + b ) 2) 8 a 3 – b 3 – 12 a 2 b + 6 ab 2 Sol: It is in the form of a 3 – b 3 – 3 ab (a – b )= ( a – b )3 Here a = 2 a , b = b 8 a 3 – b 3 – 12 a 2 b + 6 ab 2 = ( 2 a – b )3 2/28/2021 6