Question

factorise 343 x cube - 216 y cube

Answer 1

Answer:

(7x-6y) (49x^2+42xy+36y^2)

Step-by-step explanation:

Given, 343x^3-216y^3

We can also write this as (7x)^3+(6y)^3

We use the formula a^3-b^3=(a-b) (a^2+ab+b^2)

In the above question a=7x and b=6y

Applying formula, we get

(7x)^3+(6y)^3 = (7x-6y) (7x^2+(7x)(6y)+6y^2)

Simplifying,

(7x)^3+(6y)^3 = (7x-6y) (49x^2+42xy+36y^2)

Answer 2

Answer:

  (7x - 6y)  •  (49x2 + 42xy + 36y2)

Step-by-step explanation:

343x³ - 216y³ can be written as

= 343x³ -  2³3³y³

= 7³x³ - 2³3³y³

Theory : A difference of two perfect cubes,  a³ - b³ can be factored into

             (a-b) × (a²+ab+b²)

Proof :  (a-b)•(a²+ab+b²)

=  a³+a²b+ab²-ba²-b²a-b³

=  a³+(a²b-ba²)+(ab²-b²a)-b³

=  a³+0+0+b³

=  a³+b³

• 343  is the cube of  7  

• 216  is the cube of   6  

• x3 is the cube of   x1

• y3 is the cube of   y1

Factorization is :

            (7x - 6y)  •  (49x2 + 42xy + 36y2)