Question

Factorise 8x^3+729+108x^2+486x

Answer 1

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8x^3+108x^2+486x+729

(2x)^3+3(4x^2)(9)+3(2x)(81)+(9)^3

(2x)^3+3(2x)^2(9)+3(2x)9^2+(9)^3

IT IS IN THE FORM OF : (a+b)^3=a^3+3a^2b+3ab^2+b^3

Hence,the final answer is (2x+9)^3

Answer 2

8x³ + 729 + 108x² + 486 = (2x + 9)(2x + 9)(2x + 9)

Given :

The expression 8x³ + 729 + 108x² + 486

To find :

Factorise the expression

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

8x³ + 729 + 108x² + 486

Step 2 of 2 :

Factorise the expression

We are aware of the formula that

(a + b)³ = a³ + b³ + 3a²b + 3ab²

Thus we get

8x³ + 729 + 108x² + 486

$\sf = {(2x)}^{3} + {(9)}^{3} + 3 \times {(2x)}^{2} \times 9 + 3 \times 2x \times {(9)}^{2}$

$\sf = {(2x + 9)}^{3}$

$\sf = (2x + 9)(2x + 9)(2x + 9)$