Question

a^3b^3+512 factorise​

Answer 1

Answer:

a³b³ +512 = (ab + 8)(a²b² -8ab + 64)

Step-by-step explanation:

Given: a³b³+512.

To find : we have to factorise.

Solution:  The solution deals with factorising binomials as the sum or difference of cubes.

a³ b³ + 512 = a³ b³+ 8³-------eq.(1) since 512 = 8³

Theory: a sum of two perfect cubes, a³ +b³ can be factored into

(a+b)(a²-ab+b²). this is an algebraic identity.

An algebraic identity is an equality that holds for any values of its variables. They are also used for factorization of polynomials.

a³+b³ = (a+b)(a²-ab+b²)

Here a =ab and b = 8  

Now we apply this theory in eq.(1)

a³b³ + 512 = (ab + 8)(( ab)² - ab×8 + 8²)

∴ a³b³ +512  = (ab + 8)( a²b²-8ab +64)   is the required answer.

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Answer 2

Answer:

The factorisation of the equation a³b³ + 512 is (ab + 8)(a²b² - 8ab + 64).

Step-by-step explanation:

Recall the identity,

x³ + y³ = (x + y)(x² - xy + y²) . . . . . (1)

Step 1 of 1

Consider the given equation as follows:

a³b³ + 512 . . . . . (2)

The factorisation of the number 512 is:-

512 = $2\times2\times2\times2\times2\times2\times2\times2\times2$

512 = 8³

Rewrite the expression (2) as follows:

(ab)³ + 8³

Now,

Let x = ab and y = 8.

Substitute the values ab for x and 8 for y in the identity (1) as follows:

(ab)³ + 8³ = (ab + 8)((ab)² - ab(8) + 8²)

a³b³ + 512 = (ab + 8)(a²b² - 8ab + 64)

Final answer: The factorisation of a³b³ + 512 is (ab + 8)(a²b² - 8ab + 64).

#SPJ2