(5d%2B3).jpeg "(2d+4)(5d+3)")
Expanding the Expression (2d+4)(5d+3)
This article will guide you through the process of expanding the expression (2d+4)(5d+3).
Understanding the Problem
The expression (2d+4)(5d+3) is a product of two binomials. Expanding it involves multiplying each term in the first binomial by each term in the second binomial.
The Distributive Property
The key to expanding this expression is using the distributive property. This property states that for any numbers a, b, c, and d:
a(b+c) = ab + ac*
Similarly, we can apply this to our problem:
(2d+4)(5d+3) = 2d(5d+3) + 4(5d+3)
Expanding the Expression
Now, we can apply the distributive property again to each part of the equation:
- 2d(5d+3) = (2d * 5d) + (2d * 3) = 10d² + 6d
- 4(5d+3) = (4 * 5d) + (4 * 3) = 20d + 12
Combining Like Terms
Finally, we combine the like terms:
**(2d+4)(5d+3) = 10d² + 6d + 20d + 12 = ** 10d² + 26d + 12
Conclusion
Therefore, the expanded form of (2d+4)(5d+3) is 10d² + 26d + 12. This process demonstrates how the distributive property is used to multiply binomials and simplify algebraic expressions.