%5E3-standard-form.jpeg "(2c+5d)^3 Standard Form")
Expanding (2c + 5d)³: A Step-by-Step Guide
The expression (2c + 5d)³ represents the cube of the binomial (2c + 5d). To expand it into standard form, we need to apply the distributive property multiple times. Here's a breakdown of the process:
Understanding the Cube
The expression (2c + 5d)³ is equivalent to multiplying (2c + 5d) by itself three times:
(2c + 5d)³ = (2c + 5d) * (2c + 5d) * (2c + 5d)
Expanding the First Two Factors
Let's start by expanding the first two factors:
(2c + 5d) * (2c + 5d) = 4c² + 10cd + 10cd + 25d²
Simplifying, we get:
4c² + 20cd + 25d²
Expanding the Final Factor
Now, we multiply the result by the remaining factor (2c + 5d):
(4c² + 20cd + 25d²) * (2c + 5d)
Using the distributive property again:
8c³ + 40c²d + 50cd² + 20c²d + 100cd² + 125d³
Combining Like Terms
Finally, we combine like terms to get the standard form:
8c³ + 60c²d + 150cd² + 125d³
Conclusion
Therefore, the expanded form of (2c + 5d)³ in standard form is 8c³ + 60c²d + 150cd² + 125d³. This process involves using the distributive property multiple times and combining like terms to simplify the expression.