Expanding the Expression (a+b)(c+d)(e+f)(g+h)
The expression (a+b)(c+d)(e+f)(g+h) represents the product of four binomials. Expanding this expression involves multiplying out all the terms. While it might seem daunting at first, there's a systematic approach to solve this.
Understanding the Process
The key to expanding this expression lies in distributive property, which states: a(b+c) = ab + ac
We apply this property repeatedly to multiply each term in one binomial with every term in the other.
StepbyStep Expansion

Start with the first two binomials: (a+b)(c+d) = ac + ad + bc + bd

Multiply the result with the third binomial: (ac + ad + bc + bd)(e+f) = ace + acf + ade + adf + bce + bcf + bde + bdf

Finally, multiply the result with the last binomial: (ace + acf + ade + adf + bce + bcf + bde + bdf)(g+h) = aceg + aceh + acfg + acfh + adeg + adeh + adfg + adfh + bceg + bceh + bcfg + bcfh + bdeg + bdeh + bdfg + bdfh
The Final Result
The expanded form of (a+b)(c+d)(e+f)(g+h) is: aceg + aceh + acfg + acfh + adeg + adeh + adfg + adfh + bceg + bceh + bcfg + bcfh + bdeg + bdeh + bdfg + bdfh
This demonstrates that the final expression has 16 terms, each representing a unique combination of one term from each of the four original binomials.
Key Points
 The expansion process involves applying the distributive property repeatedly.
 The number of terms in the final expression is equal to 2^n, where n is the number of binomials.
 This expansion can be generalized to any number of binomials.
By understanding this process, you can easily expand any product of binomials, regardless of the number of factors involved.