Question

Simplify -: i) ( 2a + b ) ^ 3 + ( 2a - b ) ^ 3

Answer 1

hey dear use identity no11 and then aolve

Answer 2

Answer:

$(2a+b)^{3}+(2a-b)^{3}= 24a^{2}b+2b^{3}$

Step-by-step explanation:

$(2a+b)^{3}+(2a-b)^{3}$

= [(2a)³ + 3×(2a)²×b+3×2a×b² + b³]

+ [(2a)³ - 3×(2a)²×b+3×2a×b² - b³]

/* By algebraic identities :

i) (x+y)³ = x³ + 3x²y +3xy² + y³

ii) (x-y)³ = x³ - 3x²y + 3xy² - y³ */

= 8a³ + 12a²b+6ab²+b³ - (8a³ - 12a²b + 6ab² - b³)

= 8a³ + 12a²b+6ab²+b³ - 8a³ + 12a²b - 6ab² + b³

= 8a³ - 8a³ + 12a²b+12a²b+6ab²-6ab²+b³+b³

= 24a²b + 2b³

Or

= 2b( 12a² + b²)

Therefore.,

$(2a+b)^{3}+(2a-b)^{3}= 24a^{2}b+2b^{3}$

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