Question

343x^3+y^3 factor completely

Answer 1

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

Explanation:

Sure, the complete factorization of 343x^3 + y^3 is:

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

This can be factored using the sum of cubes factorization:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

where a = 7x and b = y.

The factorization is complete because it cannot be factored any further. The expression is in the form of the difference of two cubes, which is a special factorization pattern.

I hope this helps! Let me know if you have any other questions.

Answer 2

(7x + y)(49x² - 7xy + y²)

Additional Information:

Refer to the attached image for additional information about factoring cubes.

Explanation:

To factor the expression 343x³ + y³, we can use the sum of cubes formula:

=> a³ + b³ = (a + b)(a² - ab + b²)

Applying this formula to our expression, we have:

=> 343x³ + y³ = (7x)³ + (y)³

In our case,

a = 7x and b = y

Now we can rewrite it as:

=> (7x)³ + (y)³ = (7x + y)((7x)² - (7x)(y) + (y)²)

This simplifies down to:

=> (7x + y)(49x² - 7xy + y²)

We cannot factor further, thus the problem is solved.