(4x%5E2y).jpeg "(x^3+2y^2+3xy)(4x^2y)")
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.