(4-4c%5E2d).jpeg "(3-c^2d)(4-4c^2d)")
Expanding the Expression (3 - c²d)(4 - 4c²d)
This article will walk you through the process of expanding the expression (3 - c²d)(4 - 4c²d). This involves using the distributive property of multiplication.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. Mathematically, this is represented as:
a(b + c) = ab + ac
Applying the Distributive Property to (3 - c²d)(4 - 4c²d)
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Distribute the first term:
- Multiply 3 by each term inside the second parentheses:
- 3 * 4 = 12
- 3 * -4c²d = -12c²d
- Multiply 3 by each term inside the second parentheses:
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Distribute the second term:
- Multiply -c²d by each term inside the second parentheses:
- -c²d * 4 = -4c²d
- -c²d * -4c²d = 4c⁴d²
- Multiply -c²d by each term inside the second parentheses:
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Combine the results:
- Add all the terms we obtained:
- 12 - 12c²d - 4c²d + 4c⁴d²
- Add all the terms we obtained:
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Simplify by combining like terms:
- Combine the terms with c²d:
- 12 - 16c²d + 4c⁴d²
- Combine the terms with c²d:
Final Result
Therefore, the expanded form of (3 - c²d)(4 - 4c²d) is: 12 - 16c²d + 4c⁴d²