(2x−4y3)2(3x6y2)

Question

Step 1: Response area

Step 2: Response area

Step 3:

Answer 1

To simplify the given expression, we need to expand the expression and then combine like terms.

First, we expand the expression (2x - 4y^3)^2 by using the formula for squaring a binomial:

(2x - 4y^3)^2 = (2x - 4y^3)(2x - 4y^3)

Using the distributive property, we can multiply each term in the first binomial by each term in the second binomial:

(2x * 2x) + (2x * -4y^3) + (-4y^3 * 2x) + (-4y^3 * -4y^3)

Simplifying each term:

4x^2 - 8xy^3 - 8xy^3 + 16y^6

Combining like terms:

4x^2 - 16xy^3 + 16y^6

Now, we multiply this expression by (3x^6y^2):

(4x^2 - 16xy^3 + 16y^6)(3x^6y^2)

Using the distributive property again, we can multiply each term in the first expression by each term in the second expression:

(4x^2 * 3x^6y^2) + (-16xy^3 * 3x^6y^2) + (16y^6 * 3x^6y^2)

Simplifying each term:

12x^8y^2 - 48x^7y^5 + 48x^6y^8

Thus, the simplified expression is 12x^8y^2 - 48x^7y^5 + 48x^6y^8.