2 min read Jun 17, 2024

Expanding the Expression (x^3 + 2y^2 + 3xy)(4x^2y)

This article explores the expansion of the expression (x^3 + 2y^2 + 3xy)(4x^2y) using the distributive property.

The Distributive Property

The distributive property states that for any numbers a, b, and c:

a(b + c) = ab + ac

We can apply this property to expand our expression:

(x^3 + 2y^2 + 3xy)(4x^2y) = x^3(4x^2y) + 2y^2(4x^2y) + 3xy(4x^2y)

Expanding Each Term

Now, we need to multiply each term in the parentheses by 4x^2y. Remember that when multiplying exponents with the same base, you add the powers.

  • x^3(4x^2y) = 4x^(3+2)y = 4x^5y
  • 2y^2(4x^2y) = 8x^2y^(2+1) = 8x^2y^3
  • 3xy(4x^2y) = 12x^(1+2)y^(1+1) = 12x^3y^2

The Expanded Expression

Combining the expanded terms, we get the final result:

(x^3 + 2y^2 + 3xy)(4x^2y) = 4x^5y + 8x^2y^3 + 12x^3y^2

This is the expanded form of the original expression.

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