Question

343x^3y+512y^4 factorie ​

Answer 1

Step-by-step explanation:

Equation at the end of step 1

((343 • (x3)) • y) - 29y4

STEP

2

:

Equation at the end of step

2

:

(73x3 • y) - 29y4

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

343x3y - 512y4 = y • (343x3 - 512y3)

Trying to factor as a Difference of Cubes:

4.2 Factoring: 343x3 - 512y3

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 : 343 is the cube of 7

Check : 512 is the cube of 8

Check : x3 is the cube of x1

Check : y3 is the cube of y1

Factorization is :

(7x - 8y) • (49x2 + 56xy + 64y2)

Trying to factor a multi variable polynomial :

4.3 Factoring 49x2 + 56xy + 64y2

Try to factor this multi-variable trinomial using trial and error

Factorization fails

Final result :

y • (7x - 8y) • (49x2 + 56xy + 64y2)

Answer 2

Answer:

y(7x+8y) (49x^2-56xy+64y^2)

Step-by-step explanation:

(343x^3+512y^3)

y(7x+8y) (49x^2-56xy+64y^2)