Simplify the expression (x^2-2y)(x^2+2y)(square root(16y^4)+square root (x^8)).

1 Answer | Add Yours

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We notice that the product of the 1st and the second factors returns a difference of two squares:

(x^2 - 2y)(x^2 + 2y) = (x^2)^2 - (2y)^2

(x^2 - 2y)(x^2 + 2y) = x^4 - 4y^2

We'll manage the terms of the 3rd factor:

sqrt(16y^4) = 4y^2

sqrt x^8 = x^4

We'll re-write the product, rearranging the terms of the 3rd factor:

(x^4 - 4y^2)(x^4 + 4y^2)

We notice that we've get a product that returns a difference of two squares:

(x^4 - 4y^2)(x^4 + 4y^2) = (x^4)^2 - (4y^2)^2

We'll multiply the exponents:

(x^4 - 4y^2)(x^4 + 4y^2) = x^(4*2) - 16*y^(2*2)

(x^4 - 4y^2)(x^4 + 4y^2) = x^8 - 16y^4

The requested simplified expression is x^8 - 16y^4.

We’ve answered 318,944 questions. We can answer yours, too.

Ask a question