Simplify each of the following :
(i) (x+3)³ + (x-3)³
(ii) (x/2 + y/3)³ - (x/2 - y/3)³
(iii) (x + 2/x)³ + (x +2/x)³
(iv) (2x-5y)³ - (2x+5y)³
Answers
By Using identities:
a³ + b³ = (a + b)(a² + b² – ab)
a³ – b³ = (a – b)(a² + b² + ab)
(a + b)(a - b) = a² – b²
(a + b)² = a² + b² + 2ab and
(a – b)² = a² + b² – 2ab
Given (i) (x + 3)³ + (x - 3)³
Here a = (x + 3) and b = (x - 3)
= (x + 3 + x - 3){(x + 3)² + (x - 3)² - (x + 3) (x - 3)}
= 2x {x² + 3² + 2 x × 3 + x² + 3² - 2 × x × 3 - ( x² - 3²)}
= 2x {x² + 9 + 6x + x² + 9 - 6x - x² + 9}
= 2x {x² + 9 + 9 + 9}
= 2x {x² + 27}
= 2x³ + 54x
SOLUTION OF (II) , (III) & (IV) ARE IN THE ATTACHMENT BELOW.
HOPE THIS ANSWER WILL HELP YOU…..
Similar questions :
Find the cube of each of the following binomial expressions:
(i) (1/x + y/3)³
(ii) (3/x-2/x)³
(iii)(2x - 3/x)³
(iv)(4 - 1/3x)³
https://brainly.in/question/15897612
Evaluate each of the following:
(i) (103)³
(ii) (98)³
(iii) (9.9)³
(iv) (10.4)³
(v) (598)³
(vi) (99)³
https://brainly.in/question/15897789
Answer:
Step-by-step explanation:
Given (i) (x + 3)³ + (x - 3)³
Here a = (x + 3) and b = (x - 3)
= (x + 3 + x - 3){(x + 3)² + (x - 3)² - (x + 3) (x - 3)}
= 2x {x² + 3² + 2 x × 3 + x² + 3² - 2 × x × 3 - ( x² - 3²)}
= 2x {x² + 9 + 6x + x² + 9 - 6x - x² + 9}
= 2x {x² + 9 + 9 + 9}
= 2x {x² + 27}
= 2x³ + 54x