Factorize the expression y^6+26y^3-27

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justaguide | College Teacher | (Level 2) Distinguished Educator

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This question has been answered; in case you missed it here is the procedure to factorize the given expression again.

It is not possible to simplify the expression y^6 + 26y^3 - 27. If you would like it to be expressed as a product of factors that could be done.

y^6 + 26y^3 - 27

Let y^3 = x

=> x^2 + 26x - 27

=> x^2 + 27x - x - 27

=> x(x + 27) - 1(x + 27)

=> (x - 1)(x + 27)

=> (y^3 - 1)(y^3 + 27)

Use the expansions a^3 - b^3 = (a - b) (a^2+ ab + b^2) and a^3 + b^3 = (a + b) (a^2- ab + b^2)

=> (y - 1)(y^2 - 3y + 9)*(y + 3)(y^2 + y + 1)

The expression y^6 + 26y^3 - 27 as a product of factors is (y - 1)(y^2 - 3y + 9)*(y + 3)(y^2 + y + 1)

Top Answer

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

It is not possible to simplify the expression y^6 + 26y^3 - 27. If you would like it to be expressed as a product of factors that could be done.

y^6 + 26y^3 - 27

Let y^3 = x

=> x^2 + 26x - 27

=> x^2 + 27x - x - 27

=> x(x + 27) - 1(x + 27)

=> (x - 1)(x + 27)

=> (y^3 - 1)(y^3 + 27)

=> (y - 1)(y^2 - 3y + 9)*(y + 3)(y^2 + y + 1)

The expression y^6 + 26y^3 - 27 as a product of factors is (y - 1)(y^2 - 3y + 9)*(y + 3)(y^2 + y + 1)

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