Question

Factorsie : √8 x 3 – 27 y3 using a suitable identity.​

Answer 1

Step-by-step explanation:

Given :-

√8x³ -27y³

To find :-

Factorse the expression ?

Solution :-

Given expression is √8x³ -27y³

√8 = √(2×2×2) = √2×√2×√2 =(√2)³

27 = 3×3×3 = 3³

Now,

Given expression can be written as

=> (√2)³x³-3³y³

=> (√2x)³ - (3y)³

This is in the form of a³-b³

Where, a = √2 x

and b = 3y

We know that

a³-b³ = (a-b)(a²+ab+b²)

(√2x)³ - (3y)³

=> (√2 x -3y)[(√2 x)²+(√2 x)(3y) +(3y)²]

=> (√2 x -3y)(2x²+3√2 xy +9y²)

√8x³ -27y³ = (√2 x -3y)(2x²+3√2 xy +9y²)

Answer:-

The factorization of the given expression is

(√2 x -3y)(2x²+3√2 xy +9y²)

Used Identity:-

→ a³-b³ = (a-b)(a²+ab+b²)