factorise 343 x cube - 216 y cube
Answers
Answered by
6
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)
Answered by
16
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)
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