What's the value?

Algebra Level 2

If a = − 3 a= -3 and b = 2 b=2 , then find the value of 8 a 3 + 36 a 2 b + 54 a b 2 + 27 b 3 8a^3+36a^2 b+54ab^2 +27b^3 .


The answer is 0.

Munem Shahriar by Munem Shahriar , 18, Bangladesh

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4 solutions

Munem Shahriar
Mar 26, 2017

Given. a= -3 & b= 2

=8a ³ +36a²b+54ab²+27b ³

=(2a) ³ +3×(2a)²×3b+3×2a×(3b)²+(3b) ³

=(2a+3b) ³

={2(-3)+3 . 2} ³

=(-6+6) ³ =0 ³ =0

ans. 0

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Mohammad Khaza
Jul 21, 2017

Given that, a= -3 & b= 2

now,8a³+36a²b+54ab²+27b³

=(2a)³+3×(2a)²×3b+3×2a×(3b)²+(3b)³

=(2a+3b)³

={2(-3)+3. 2}³

=(-6+6)³=0³=0

so, the answer is 0

2 Helpful 0 Interesting 0 Brilliant 0 Confused

8 a^3+36 a^2 b+54 a b^2+27 b^3 =>(2 a)^3+3 (2 a) (3 b) (2 a+3 b)+(3 b)^3 =>(2 a+3 b)^3 =>(2 (-3)+3*(2))^3 =>(0)^3=0

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Ankit Kumar Jain
Aug 18, 2017

It can be observed easily that the expression is ( 2 a + 3 b ) 3 (2a+3b)^3 where a = − 3 , b = 2 a = -3 , b = 2 .

Therefore our answer is 0 \boxed{0}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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