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

2 min read Jun 16, 2024
(2x^2y)^2+3x^4y^3-6x^3y^2 (xy)^2

Simplifying the Expression: (2x^2y)^2 + 3x^4y^3 - 6x^3y^2 (xy)^2

This expression involves several terms with exponents and variables. To simplify it, we'll use the rules of exponents and then combine like terms.

Step 1: Simplify each term individually

  • (2x^2y)^2: Applying the power of a product rule, we square each factor inside the parentheses:

    • (2)^2 = 4
    • (x^2)^2 = x^(2*2) = x^4
    • (y)^2 = y^2
    • Therefore, (2x^2y)^2 = 4x^4y^2

  • 3x^4y^3: This term is already in its simplest form.

  • 6x^3y^2 (xy)^2:

    • First, simplify (xy)^2 = x^2y^2
    • Then, multiply the coefficients and combine the variables: 6x^3y^2 * x^2y^2 = 6x^5y^4

Step 2: Combine like terms

Now we have the simplified expression: 4x^4y^2 + 3x^4y^3 - 6x^5y^4

Since there are no other like terms (terms with the same variables and exponents), this is the final simplified form.

Therefore, the simplified expression is 4x^4y^2 + 3x^4y^3 - 6x^5y^4.

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