Question

10. Factorise 64 x3 – 343 y3​

Answer 1

Step-by-step explanation:

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

Check : 64 is the cube of 4

Check : 343 is the cube of 7

Check : x3 is the cube of x1

Check : y3 is the cube of y1

Factorization is :

(4x - 7y) • (16x2 + 28xy + 49y2)

Trying to factor a multi variable polynomial :

3.2 Factoring 16x2 + 28xy + 49y2

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