(c%2Bd)(e%2Bf)(g%2Bh).jpeg "(a+b)(c+d)(e+f)(g+h)")
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.
Step-by-Step Expansion
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Start with the first two binomials: (a+b)(c+d) = ac + ad + bc + bd
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Multiply the result with the third binomial: (ac + ad + bc + bd)(e+f) = ace + acf + ade + adf + bce + bcf + bde + bdf
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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.