Question

(2a + 3b)^3

Evaluate

Answer 1

$\huge\mathfrak\red{Solution}$

Here first we have to know the formula.

Solving it by identity :

( a + b )³ = a³ + 3a²b + 3ab² + b³

So here given that :

a = 2a

b = 3b

Then According to identity :

( 2a + 3b)³ = (2a) ³ + 3 * (2a) ² * 3b + 3 * 2a * (3b) ² + (3b) ³

( 2a + 3b ) ³ = 8a³ + 36a²b + 54ab² + 27b³

Here is your equation of ( 2a + 3b)³ is 8a³ + 36a²b + 54ab² + 27b³

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Answer 2

Answer:

$\boxed{8a^3 + 27b^3 + 36a^2b + 54ab^2}$

Step-by-step explanation:

Its an algebraic identity.

$(x+y)^3 = x^3 + y^3 + 3xy(x+y)$

Let's prove this.

$(x+y)^3\\\\= (x+y)^2(x+y)$

We know that

$(x+y)^2 = x^2 + y^2 + 2xy$

So, we have

$(x^2 + y^2 + 2xy)(x+ y)\\\\\text{On multiplying, we have}\\\\x^3 + xy^2 + 2x^2y + x^2y+y^3 + 2xy^2\\\\= x^3 + y^3 + 3xy^2 + 3x^2y\\\\= x^3 + y^3 + 3xy(x+y)$

This proves the above algebraic identity.

The evaluation of (2a + 3b)³ will also be done using this identity.

Let's do it...

$(2a+ 3b)^3 = (2a)^3 + (3b)^3 + 3(2a)(3b)(2a+3b)\\\\= 8a^3 + 27b^3 + 18ab(2a+3b)\\\\= \boxed{8a^3 + 27b^3 + 36a^2b + 54ab^2}$

That's the answer to your question.

Thanks!